text
stringlengths 89
2.49k
| category
stringclasses 19
values |
|---|---|
Long Range Order at Low Temperature in Dipolar Spin Ice: Recently it has been suggested that long range magnetic dipolar interactions
are responsible for spin ice behavior in the Ising pyrochlore magnets ${\rm
Dy_{2}Ti_{2}O_{7}}$ and ${\rm Ho_{2}Ti_{2}O_{7}}$. We report here numerical
results on the low temperature properties of the dipolar spin ice model,
obtained via a new loop algorithm which greatly improves the dynamics at low
temperature. We recover the previously reported missing entropy in this model,
and find a first order transition to a long range ordered phase with zero total
magnetization at very low temperature. We discuss the relevance of these
results to ${\rm Dy_{2}Ti_{2}O_{7}}$ and ${\rm Ho_{2}Ti_{2}O_{7}}$. | cond-mat_dis-nn |
Storage properties of a quantum perceptron: Driven by growing computational power and algorithmic developments, machine
learning methods have become valuable tools for analyzing vast amounts of data.
Simultaneously, the fast technological progress of quantum information
processing suggests employing quantum hardware for machine learning purposes.
Recent works discuss different architectures of quantum perceptrons, but the
abilities of such quantum devices remain debated. Here, we investigate the
storage capacity of a particular quantum perceptron architecture by using
statistical mechanics techniques and connect our analysis to the theory of
classical spin glasses. We focus on a specific quantum perceptron model and
explore its storage properties in the limit of a large number of inputs.
Finally, we comment on using statistical physics techniques for further studies
of neural networks. | cond-mat_dis-nn |
Viscosity and relaxation processes of the liquid become amorphous
Al-Ni-REM alloys: The temperature and time dependencies of viscosity of the liquid alloys,
Al87Ni8Y5, Al86Ni8La6, Al86Ni8Ce6, and the binary Al-Ni and Al-Y melts with Al
concentration over 90 at.% have been studied. Non-monotonic relaxation
processes caused by destruction of nonequilibrium state inherited from the
basic-heterogeneous alloy have been found to take place in Al-Y, Al-Ni-REM
melts after the phase solid-liquid transition. The mechanism of nonmonotonic
relaxation in non-equilibrium melts has been suggested. | cond-mat_dis-nn |
Random Networks of Spiking Neurons: Instability in the Xenopus tadpole
moto-neural pattern: A large network of integrate-and-fire neurons is studied analytically when
the synaptic weights are independently randomly distributed according to a
Gaussian distribution with arbitrary mean and variance. The relevant order
parameters are identified, and it is shown that such network is statistically
equivalent to an ensemble of independent integrate-and-fire neurons with each
input signal given by the sum of a self-interaction deterministic term and a
Gaussian colored noise. The model is able to reproduce the quasi-synchronous
oscillations, and the dropout of their frequency, of the central nervous system
neurons of the swimming Xenopus tadpole. Predictions from the model are
proposed for future experiments. | cond-mat_dis-nn |
The Hidden Landscape of Localization: Wave localization occurs in all types of vibrating systems, in acoustics,
mechanics, optics, or quantum physics. It arises either in systems of irregular
geometry (weak localization) or in disordered systems (Anderson localization).
We present here a general theory that explains how the system geometry and the
wave operator interplay to give rise to a "landscape" that splits the system
into weakly coupled subregions, and how these regions shape the spatial
distribution of the vibrational eigenmodes. This theory holds in any dimension,
for any domain shape, and for all operators deriving from an energy form. It
encompasses both weak and Anderson localizations in the same mathematical frame
and shows, in particular, that Anderson localization can be understood as a
special case of weak localization in a very rough landscape. | cond-mat_dis-nn |
Multifractality and self-averaging at the many-body localization
transition: Finite-size effects have been a major and justifiable source of concern for
studies of many-body localization, and several works have been dedicated to the
subject. In this paper, however, we discuss yet another crucial problem that
has received much less attention, that of the lack of self-averaging and the
consequent danger of reducing the number of random realizations as the system
size increases. By taking this into account and considering ensembles with a
large number of samples for all system sizes analyzed, we find that the
generalized dimensions of the eigenstates of the disordered Heisenberg spin-1/2
chain close to the transition point to localization are described remarkably
well by an exact analytical expression derived for the non-interacting
Fibonacci lattice, thus providing an additional tool for studies of many-body
localization. | cond-mat_dis-nn |
Asymptotically exact theory for nonlinear spectroscopy of random quantum
magnets: We study nonlinear response in quantum spin systems {near infinite-randomness
critical points}. Nonlinear dynamical probes, such as two-dimensional (2D)
coherent spectroscopy, can diagnose the nearly localized character of
excitations in such systems. {We present exact results for nonlinear response
in the 1D random transverse-field Ising model, from which we extract
information about critical behavior that is absent in linear response. Our
analysis yields exact scaling forms for the distribution functions of
relaxation times that result from realistic channels for dissipation in random
magnets}. We argue that our results capture the scaling of relaxation times and
nonlinear response in generic random quantum magnets in any spatial dimension. | cond-mat_dis-nn |
Of symmetries, symmetry classes, and symmetric spaces: from disorder and
quantum chaos to topological insulators: Quantum mechanical systems with some degree of complexity due to multiple
scattering behave as if their Hamiltonians were random matrices. Such behavior,
while originally surmised for the interacting many-body system of highly
excited atomic nuclei, was later discovered in a variety of situations
including single-particle systems with disorder or chaos. A fascinating theme
in this context is the emergence of universal laws for the fluctuations of
energy spectra and transport observables. After an introduction to the basic
phenomenology, the talk highlights the role of symmetries for universality, in
particular the correspondence between symmetry classes and symmetric spaces
that led to a classification scheme dubbed the 'Tenfold Way'. Perhaps
surprisingly, the same scheme has turned out to organize also the world of
topological insulators. | cond-mat_dis-nn |
Minimal contagious sets in random regular graphs: The bootstrap percolation (or threshold model) is a dynamic process modelling
the propagation of an epidemic on a graph, where inactive vertices become
active if their number of active neighbours reach some threshold. We study an
optimization problem related to it, namely the determination of the minimal
number of active sites in an initial configuration that leads to the activation
of the whole graph under this dynamics, with and without a constraint on the
time needed for the complete activation. This problem encompasses in special
cases many extremal characteristics of graphs like their independence,
decycling or domination number, and can also be seen as a packing problem of
repulsive particles. We use the cavity method (including the effects of replica
symmetry breaking), an heuristic technique of statistical mechanics many
predictions of which have been confirmed rigorously in the recent years. We
have obtained in this way several quantitative conjectures on the size of
minimal contagious sets in large random regular graphs, the most striking being
that 5-regular random graph with a threshold of activation of 3 (resp.
6-regular with threshold 4) have contagious sets containing a fraction 1/6
(resp. 1/4) of the total number of vertices. Equivalently these numbers are the
minimal fraction of vertices that have to be removed from a 5-regular (resp.
6-regular) random graph to destroy its 3-core. We also investigated Survey
Propagation like algorithmic procedures for solving this optimization problem
on single instances of random regular graphs. | cond-mat_dis-nn |
Acoustic Cloak Design via Machine Learning: Acoustic metamaterials are engineered microstructures with special mechanical
and acoustic properties enabling exotic effects such as wave steering, focusing
and cloaking. The design of acoustic cloaks using scattering cancellation has
traditionally involved the optimization of metamaterial structure based on
direct computer simulations of the total scattering cross section (TSCS) for a
large number of configurations. Here, we work with sets of cylindrical objects
confined in a region of space and use machine learning methods to streamline
the design of 2D configurations of scatterers with minimal TSCS demonstrating
cloaking effect at discrete sets of wavenumbers. After establishing that
artificial neural networks are capable of learning the TSCS based on the
location of cylinders, we develop an inverse design algorithm, combining
variational autoencoders and the Gaussian process, for predicting optimal
arrangements of scatterers given the TSCS. We show results for up to eight
cylinders and discuss the efficiency and other advantages of the machine
learning approach. | cond-mat_dis-nn |
Tunneling probe of fluctuating superconductivity in disordered thin
films: Disordered thin films close to the superconducting-insulating phase
transition (SIT) hold the key to understanding quantum phase transition in
strongly correlated materials. The SIT is governed by superconducting quantum
fluctuations, which can be revealed for example by tunneling measurements.
These experiments detect a spectral gap, accompanied by suppressed coherence
peaks that do not fit the BCS prediction. To explain these observations, we
consider the effect of finite-range superconducting fluctuations on the density
of states, focusing on the insulating side of the SIT. We perform a controlled
diagrammatic resummation and derive analytic expressions for the tunneling
differential conductance. We find that short-range superconducting fluctuations
suppress the coherence peaks, even in the presence of long-range correlations.
Our approach offers a quantitative description of existing measurements on
disordered thin films and accounts for tunneling spectra with suppressed
coherence peaks observed, for example, in the pseudo gap regime of
high-temperature superconductors. | cond-mat_dis-nn |
Finite-size scaling analysis of localization transition for scalar waves
in a 3D ensemble of resonant point scatterers: We use the random Green's matrix model to study the scaling properties of the
localization transition for scalar waves in a three-dimensional (3D) ensemble
of resonant point scatterers. We show that the probability density $p(g)$ of
normalized decay rates of quasi-modes $g$ is very broad at the transition and
in the localized regime and that it does not obey a single-parameter scaling
law for finite system sizes that we can access. The single-parameter scaling
law holds, however, for the small-$g$ part of $p(g)$ which we exploit to
estimate the critical exponent $\nu$ of the localization transition.
Finite-size scaling analysis of small-$q$ percentiles $g_q$ of $p(g)$ yields an
estimate $\nu \simeq 1.55 \pm 0.07$. This value is consistent with previous
results for Anderson transition in the 3D orthogonal universality class and
suggests that the localization transition under study belongs to the same
class. | cond-mat_dis-nn |
Mixed spectra and partially extended states in a two-dimensional
quasiperiodic model: We introduce a two-dimensional generalisation of the quasiperiodic
Aubry-Andr\'e model. Even though this model exhibits the same duality relation
as the one-dimensional version, its localisation properties are found to be
substantially more complex. In particular, partially extended single-particle
states appear for arbitrarily strong quasiperiodic modulation. They are
concentrated on a network of low-disorder lattice lines, while the rest of the
lattice hosts localised states. This spatial separation protects the localised
states from delocalisation, so no mobility edge emerges in the spectrum.
Instead, localised and partially extended states are interspersed, giving rise
to an unusual type of mixed spectrum and enabling complex dynamics even in the
absence of interactions. A striking example is ballistic transport across the
low-disorder lines while the rest of the system remains localised. This
behaviour is robust against disorder and other weak perturbations. Our model is
thus directly amenable to experimental studies and promises fascinating
many-body localisation properties. | cond-mat_dis-nn |
How many longest increasing subsequences are there?: We study the entropy $S$ of longest increasing subsequences (LIS), i.e., the
logarithm of the number of distinct LIS. We consider two ensembles of
sequences, namely random permutations of integers and sequences drawn i.i.d.\
from a limited number of distinct integers. Using sophisticated algorithms, we
are able to exactly count the number of LIS for each given sequence.
Furthermore, we are not only measuring averages and variances for the
considered ensembles of sequences, but we sample very large parts of the
probability distribution $p(S)$ with very high precision. Especially, we are
able to observe the tails of extremely rare events which occur with
probabilities smaller than $10^{-600}$. We show that the distribution of the
entropy of the LIS is approximately Gaussian with deviations in the far tails,
which might vanish in the limit of long sequences. Further we propose a
large-deviation rate function which fits best to our observed data. | cond-mat_dis-nn |
Anisotropic spin relaxation in $n$-GaAs from strong inhomogeneous
hyperfine fields produced by the dynamical polarization of nuclei: The hyperfine field from dynamically polarized nuclei in n-GaAs is very
spatially inhomogeneous, as the nu- clear polarization process is most
efficient near the randomly-distributed donors. Electrons with polarized spins
traversing the bulk semiconductor will experience this inhomogeneous hyperfine
field as an effective fluctuating spin precession rate, and thus the spin
polarization of an electron ensemble will relax. A theory of spin relaxation
based on the theory of random walks is applied to such an ensemble precessing
in an oblique magnetic field, and the precise form of the (unequal)
longitudinal and transverse spin relaxation analytically derived. To
investigate this mechanism, electrical three-terminal Hanle measurements were
performed on epitaxially grown Co$_2$MnSi/$n$-GaAs heterostructures fabricated
into electrical spin injection devices. The proposed anisotropic spin
relaxation mechanism is required to satisfactorily describe the Hanle
lineshapes when the applied field is oriented at large oblique angles. | cond-mat_dis-nn |
Classical Quantum Optimization with Neural Network Quantum States: The classical simulation of quantum systems typically requires exponential
resources. Recently, the introduction of a machine learning-based wavefunction
ansatz has led to the ability to solve the quantum many-body problem in regimes
that had previously been intractable for existing exact numerical methods.
Here, we demonstrate the utility of the variational representation of quantum
states based on artificial neural networks for performing quantum optimization.
We show empirically that this methodology achieves high approximation ratio
solutions with polynomial classical computing resources for a range of
instances of the Maximum Cut (MaxCut) problem whose solutions have been encoded
into the ground state of quantum many-body systems up to and including 256
qubits. | cond-mat_dis-nn |
Absence of diffusion in certain random lattices: Numerical evidence: We demonstrate, by solving numerically the time-dependent Schroedinger
equation, the physical character of electron localization in a disordered
two-dimensional lattice. We show, in agreement with the prediction of P. W.
Anderson, that the disorder prevents electron diffusion. The electron becomes
spatially localized in a specific area of the system. Our numerical analysis
confirms that the electron localization is a quantum effect caused by the wave
character of electron propagation and has no analogy in classical mechanics. | cond-mat_dis-nn |
Return probability: Exponential versus Gaussian decay: We analyze, both analytically and numerically, the time-dependence of the
return probability in closed systems of interacting particles. Main attention
is paid to the interplay between two regimes, one of which is characterized by
the Gaussian decay of the return probability, and another one is the well known
regime of the exponential decay. Our analytical estimates are confirmed by the
numerical data obtained for two models with random interaction. In view of
these results, we also briefly discuss the dynamical model which was recently
proposed for the implementation of a quantum computation. | cond-mat_dis-nn |
One+Infinite Dimensional Attractor Neural Networks: We solve a class of attractor neural network models with a mixture of 1D
nearest-neighbour and infinite-range interactions, which are of a Hebbian-type
form. Our solution is based on a combination of mean-field methods, transfer
matrices and 1D random-field techniques, and is obtained for Boltzmann-type
equilibrium (following sequential Glauber dynamics) and Peretto-type
equilibrium (following parallel dynamics). Competition between the alignment
forces mediated via short-range interactions, and those mediated via
infinite-range ones, is found to generate novel phenomena, such as multiple
locally stable `pure' states, first-order transitions between recall states,
2-cycles and non-recall states, and domain formation leading to extremely long
relaxation times. We test our results against numerical simulations and simple
benchmark cases and find excellent agreement. | cond-mat_dis-nn |
Virtual Node Graph Neural Network for Full Phonon Prediction: The structure-property relationship plays a central role in materials
science. Understanding the structure-property relationship in solid-state
materials is crucial for structure design with optimized properties. The past
few years witnessed remarkable progress in correlating structures with
properties in crystalline materials, such as machine learning methods and
particularly graph neural networks as a natural representation of crystal
structures. However, significant challenges remain, including predicting
properties with complex unit cells input and material-dependent,
variable-length output. Here we present the virtual node graph neural network
to address the challenges. By developing three types of virtual node approaches
- the vector, matrix, and momentum-dependent matrix virtual nodes, we achieve
direct prediction of $\Gamma$-phonon spectra and full dispersion only using
atomic coordinates as input. We validate the phonon bandstructures on various
alloy systems, and further build a $\Gamma$-phonon database containing over
146,000 materials in the Materials Project. Our work provides an avenue for
rapid and high-quality prediction of phonon spectra and bandstructures in
complex materials, and enables materials design with superior phonon properties
for energy applications. The virtual node augmentation of graph neural networks
also sheds light on designing other functional properties with a new level of
flexibility. | cond-mat_dis-nn |
Synchrony and variability induced by spatially correlated additive and
multiplicative noise in the coupled Langevin model: The synchrony and variability have been discussed of the coupled Langevin
model subjected to spatially correlated additive and multiplicative noise. We
have employed numerical simulations and the analytical augmented-moment method
which is the second-order moment method for local and global variables [H.
Hasegawa, Phys. Rev. E {\bf 67}, 041903 (2003)]. It has been shown that the
synchrony of an ensemble is increased (decreased) by a positive (negative)
spatial correlation in both additive and multiplicative noise. Although the
variability for local fluctuations is almost insensitive to spatial
correlations, that for global fluctuations is increased (decreased) by positive
(negative) correlations. When a pulse input is applied, the synchrony is
increased for the correlated multiplicative noise, whereas it may be decreased
for correlated additive noise coexisting with uncorrelated multiplicative
noise. An application of our study to neuron ensembles has demonstrated the
possibility that information is conveyed by the variance and synchrony in input
signals, which accounts for some neuronal experiments. | cond-mat_dis-nn |
Can the dynamics of an atomic glass-forming system be described as a
continuous time random walk?: We show that the dynamics of supercooled liquids, analyzed from computer
simulations of the binary mixture Lennard-Jones system, can be described in
terms of a continuous time random walk (CTRW). The required discretization
comes from mapping the dynamics on transitions between metabasins. This
comparison involves verifying the conditions of the CTRW as well as a
quantitative test of the predictions. In particular it is possible to express
the wave vector-dependence of the relaxation time as well as the degree of
non-exponentiality in terms of the first three moments of the waiting time
distribution. | cond-mat_dis-nn |
Replacing neural networks by optimal analytical predictors for the
detection of phase transitions: Identifying phase transitions and classifying phases of matter is central to
understanding the properties and behavior of a broad range of material systems.
In recent years, machine-learning (ML) techniques have been successfully
applied to perform such tasks in a data-driven manner. However, the success of
this approach notwithstanding, we still lack a clear understanding of ML
methods for detecting phase transitions, particularly of those that utilize
neural networks (NNs). In this work, we derive analytical expressions for the
optimal output of three widely used NN-based methods for detecting phase
transitions. These optimal predictions correspond to the results obtained in
the limit of high model capacity. Therefore, in practice they can, for example,
be recovered using sufficiently large, well-trained NNs. The inner workings of
the considered methods are revealed through the explicit dependence of the
optimal output on the input data. By evaluating the analytical expressions, we
can identify phase transitions directly from experimentally accessible data
without training NNs, which makes this procedure favorable in terms of
computation time. Our theoretical results are supported by extensive numerical
simulations covering, e.g., topological, quantum, and many-body localization
phase transitions. We expect similar analyses to provide a deeper understanding
of other classification tasks in condensed matter physics. | cond-mat_dis-nn |
Interaction corrections to the Hall coefficient at intermediate
temperatures: We investigate the effect of electron-electron interaction on the temperature
dependence of the Hall coefficient of 2D electron gas at arbitrary relation
between the temperature $T$ and the elastic mean-free time $\tau$. At small
temperature $T\tau \ll \hbar$ we reproduce the known relation between the
logarithmic temperature dependences of the Hall coefficient and of the
longitudinal conductivity. At higher temperatures, this relation is violated
quite rapidly; correction to the Hall coefficient becomes $\propto 1/T$ whereas
the longitudinal conductivity becomes linear in temperature. | cond-mat_dis-nn |
Energy relaxation rate of 2D hole gas in GaAs/InGaAs/GaAs quantum well
within wide range of conductivitiy: The nonohmic conductivity of 2D hole gas (2DHG) in single
$GaAsIn_{0.2}Ga_{0.8}AsGaAs$ quantum well structures within the temperature
range of 1.4 - 4.2K, the carrier's densities $p=(1.5-8)\cdot10^{15}m^{-2}$ and
a wide range of conductivities $(10^{-4}-100)G_0$ ($G_0=e^2/\pi\,h$) was
investigated. It was shown that at conductivity $\sigma>G_0$ the energy
relaxation rate $P(T_h,T_L)$ is well described by the conventional theory (P.J.
Price J. Appl. Phys. 53, 6863 (1982)), which takes into account scattering on
acoustic phonons with both piezoelectric and deformational potential coupling
to holes. At the conductivity range $0.01G_0<\sigma<G_0$ energy the relaxation
rate significantly deviates down from the theoretical value. The analysis of
$\frac{dP}{d\sigma}$ at different lattice temperature $T_L$ shows that this
deviation does not result from crossover to the hopping conductivity, which
occurs at $\sigma<10^{-2}$, but from the Pippard ineffectiveness. | cond-mat_dis-nn |
The metal-insulator transition in amorphous Si_{1-x}Ni_x: Evidence for
Mott's minimum metallic conductivity: We study the metal-insulator transition in two sets of amorphous Si_{1-x}Ni_x
films. The sets were prepared by different, electron-beam-evaporation-based
technologies: evaporation of the alloy, and gradient deposition from separate
Ni and Si crucibles. The characterization included electron and scanning
tunneling microscopy, glow discharge optical emission spectroscopy, and
Rutherford back scattering. Investigating the logarithmic temperature
derivative of the conductivity, w = d ln sigma / d ln T, we observe that, for
insulating samples, w(T) shows a minimum increasing at both low and high T.
Both the minimum value of w and the corresponding temperature seem to tend to
zero as the transition is approached. The analysis of this feature of w(T,x)
leads to the conclusion that the transition in Si_{1-x}Ni_x is very likely
discontinuous at zero temperature in agreement with Mott's original views. | cond-mat_dis-nn |
A Neural Networks study of the phase transitions of Potts model: Using the techniques of Neural Networks (NN), we study the three-dimensional
(3D) 5-state ferromagnetic Potts model on the cubic lattice as well as the
two-dimensional (2D) 3-state antiferromagnetic Potts model on the square
lattice. Unlike the conventional approach, here we follow the idea employed in
Ann.~Phy.~391 (2018) 312-331. Specifically, instead of numerically generating
numerous objects for the training, the whole or part of the theoretical ground
state configurations of the studied models are considered as the training sets.
Remarkably, our investigation of these two models provides convincing evidence
for the effectiveness of the method of preparing training sets used in this
study. In particular, the results of the 3D model obtained here imply that the
NN approach is as efficient as the traditional method since the signal of a
first order phase transition, namely tunneling between two channels, determined
by the NN method is as strong as that calculated with the Monte Carlo
technique. Furthermore, the outcomes associated with the considered 2D system
indicate even little partial information of the ground states can lead to
conclusive results regarding the studied phase transition. The achievements
reached in our investigation demonstrate that the performance of NN, using
certain amount of the theoretical ground state configurations as the training
sets, is impressive. | cond-mat_dis-nn |
Excited-Eigenstate Entanglement Properties of XX Spin Chains with Random
Long-Range Interactions: Quantum information theoretical measures are useful tools for characterizing
quantum dynamical phases. However, employing them to study excited states of
random spin systems is a challenging problem. Here, we report results for the
entanglement entropy (EE) scaling of excited eigenstates of random XX
antiferromagnetic spin chains with long-range (LR) interactions decaying as a
power law with distance with exponent $\alpha$. To this end, we extend the
real-space renormalization group technique for excited states (RSRG-X) to solve
this problem with LR interaction. For comparison, we perform numerical exact
diagonalization (ED) calculations. From the distribution of energy level
spacings, as obtained by ED for up to $N\sim 18$ spins, we find indications of
a delocalization transition at $\alpha_c \approx 1$ in the middle of the energy
spectrum. With RSRG-X and ED, we show that for $\alpha>\alpha^*$ the
entanglement entropy (EE) of excited eigenstates retains a logarithmic
divergence similar to the one observed for the ground state of the same model,
while for $\alpha<\alpha^*$ EE displays an algebraic growth with the subsystem
size $l$, $S_l\sim l^{\beta}$, with $0<\beta<1$. We find that $\alpha^* \approx
1$ coincides with the delocalization transition $\alpha_c$ in the middle of the
many-body spectrum. An interpretation of these results based on the structure
of the RG rules is proposed, which is due to {\it rainbow} proliferation for
very long-range interactions $\alpha\ll 1$. We also investigate the effective
temperature dependence of the EE allowing us to study the half-chain
entanglement entropy of eigenstates at different energy densities, where we
find that the crossover in EE occurs at $\alpha^* < 1$. | cond-mat_dis-nn |
Consistency capacity of reservoir computers: We study the propagation and distribution of information-carrying signals
injected in dynamical systems serving as a reservoir computers. A multivariate
correlation analysis in tailored replica tests reveals consistency spectra and
capacities of a reservoir. These measures provide a high-dimensional portrait
of the nonlinear functional dependence on the inputs. For multiple inputs a
hierarchy of capacity measures characterizes the interference of signals from
each source. For each input the time-resolved capacity forms a nonlinear fading
memory profile. We illustrate the methodology with various types of echo state
networks. | cond-mat_dis-nn |
Fano Resonances in Flat Band Networks: Linear wave equations on Hamiltonian lattices with translational invariance
are characterized by an eigenvalue band structure in reciprocal space. Flat
band lattices have at least one of the bands completely dispersionless. Such
bands are coined flat bands. Flat bands occur in fine-tuned networks, and can
be protected by (e.g. chiral) symmetries. Recently a number of such systems
were realized in structured optical systems, exciton-polariton condensates, and
ultracold atomic gases. Flat band networks support compact localized modes.
Local defects couple these compact modes to dispersive states and generate Fano
resonances in the wave propagation. Disorder (i.e. a finite density of defects)
leads to a dense set of Fano defects, and to novel scaling laws in the
localization length of disordered dispersive states. Nonlinearities can
preserve the compactness of flat band modes, along with renormalizing (tuning)
their frequencies. These strictly compact nonlinear excitations induce tunable
Fano resonances in the wave propagation of a nonlinear flat band lattice. | cond-mat_dis-nn |
Identification of phases in scale-free networks: There is a pressing need for a description of complex systems that includes
considerations of the underlying network of interactions, for a diverse range
of biological, technological and other networks. In this work relationships
between second-order phase transitions and the power laws associated with
scale-free networks are directly quantified. A unique unbiased partitioning of
complex networks (exemplified in this work by software architectures) into
high- and low-connectivity regions can be made. Other applications to finance
and aerogels are outlined. | cond-mat_dis-nn |
The spike-timing-dependent learning rule to encode spatiotemporal
patterns in a network of spiking neurons: We study associative memory neural networks based on the Hodgkin-Huxley type
of spiking neurons. We introduce the spike-timing-dependent learning rule, in
which the time window with the negative part as well as the positive part is
used to describe the biologically plausible synaptic plasticity. The learning
rule is applied to encode a number of periodical spatiotemporal patterns, which
are successfully reproduced in the periodical firing pattern of spiking neurons
in the process of memory retrieval. The global inhibition is incorporated into
the model so as to induce the gamma oscillation. The occurrence of gamma
oscillation turns out to give appropriate spike timings for memory retrieval of
discrete type of spatiotemporal pattern. The theoretical analysis to elucidate
the stationary properties of perfect retrieval state is conducted in the limit
of an infinite number of neurons and shows the good agreement with the result
of numerical simulations. The result of this analysis indicates that the
presence of the negative and positive parts in the form of the time window
contributes to reduce the size of crosstalk term, implying that the time window
with the negative and positive parts is suitable to encode a number of
spatiotemporal patterns. We draw some phase diagrams, in which we find various
types of phase transitions with change of the intensity of global inhibition. | cond-mat_dis-nn |
On quantum and relativistic mechanical analogues in mean field spin
models: Conceptual analogies among statistical mechanics and classical (or quantum)
mechanics often appeared in the literature. For classical two-body mean field
models, an analogy develops into a proper identification between the free
energy of Curie-Weiss type magnetic models and the Hamilton-Jacobi action for a
one dimensional mechanical system. Similarly, the partition function plays the
role of the wave function in quantum mechanics and satisfies the heat equation
that plays, in this context, the role of the Schrodinger equation in quantum
mechanics. We show that this identification can be remarkably extended to
include a wide family of magnetic models classified by normal forms of suitable
real algebraic dispersion curves. In all these cases, the model turns out to be
completely solvable as the free energy as well as the order parameter are
obtained as solutions of an integrable nonlinear PDE of Hamilton-Jacobi type.
We observe that the mechanical analog of these models can be viewed as the
relativistic analog of the Curie-Weiss model and this helps to clarify the
connection between generalised self-averaging and in statistical thermodynamics
and the semi-classical dynamics of viscous conservation laws. | cond-mat_dis-nn |
Kinetic growth walks on complex networks: Kinetically grown self-avoiding walks on various types of generalized random
networks have been studied. Networks with short- and long-tailed degree
distributions $P(k)$ were considered ($k$, degree or connectivity), including
scale-free networks with $P(k) \sim k^{-\gamma}$. The long-range behaviour of
self-avoiding walks on random networks is found to be determined by finite-size
effects. The mean self-intersection length of non-reversal random walks, $<l>$,
scales as a power of the system size $N$: $<l > \sim N^{\beta}$, with an
exponent $\beta = 0.5$ for short-tailed degree distributions and $\beta < 0.5$
for scale-free networks with $\gamma < 3$. The mean attrition length of kinetic
growth walks, $<L>$, scales as $<L > \sim N^{\alpha}$, with an exponent
$\alpha$ which depends on the lowest degree in the network. Results of
approximate probabilistic calculations are supported by those derived from
simulations of various kinds of networks. The efficiency of kinetic growth
walks to explore networks is largely reduced by inhomogeneity in the degree
distribution, as happens for scale-free networks. | cond-mat_dis-nn |
Fermionic many-body localization for random and quasiperiodic systems in
the presence of short- and long-range interactions: We study many-body localization (MBL) for interacting one-dimensional lattice
fermions in random (Anderson) and quasiperiodic (Aubry-Andre) models, focusing
on the role of interaction range. We obtain the MBL quantum phase diagrams by
calculating the experimentally relevant inverse participation ratio (IPR) at
half-filling using exact diagonalization methods and extrapolating to the
infinite system size. For short-range interactions, our results produce in the
phase diagram a qualitative symmetry between weak and strong interaction
limits. For long-range interactions, no such symmetry exists as the strongly
interacting system is always many-body localized, independent of the effective
disorder strength, and the system is analogous to a pinned Wigner crystal. We
obtain various scaling exponents for the IPR, suggesting conditions for
different MBL regimes arising from interaction effects. | cond-mat_dis-nn |
An associative memory of Hodgkin-Huxley neuron networks with
Willshaw-type synaptic couplings: An associative memory has been discussed of neural networks consisting of
spiking N (=100) Hodgkin-Huxley (HH) neurons with time-delayed couplings, which
memorize P patterns in their synaptic weights. In addition to excitatory
synapses whose strengths are modified after the Willshaw-type learning rule
with the 0/1 code for quiescent/active states, the network includes uniform
inhibitory synapses which are introduced to reduce cross-talk noises. Our
simulations of the HH neuron network for the noise-free state have shown to
yield a fairly good performance with the storage capacity of $\alpha_c = P_{\rm
max}/N \sim 0.4 - 2.4$ for the low neuron activity of $f \sim 0.04-0.10$. This
storage capacity of our temporal-code network is comparable to that of the
rate-code model with the Willshaw-type synapses. Our HH neuron network is
realized not to be vulnerable to the distribution of time delays in couplings.
The variability of interspace interval (ISI) of output spike trains in the
process of retrieving stored patterns is also discussed. | cond-mat_dis-nn |
Valley Hall effect in disordered monolayer MoS2 from first principles: Electrons in certain two-dimensional crystals possess a pseudospin degree of
freedom associated with the existence of two inequivalent valleys in the
Brillouin zone. If, as in monolayer MoS2, inversion symmetry is broken and
time-reversal symmetry is present, equal and opposite amounts of k-space Berry
curvature accumulate in each of the two valleys. This is conveniently
quantified by the integral of the Berry curvature over a single valley - the
valley Hall conductivity. We generalize this definition to include
contributions from disorder described with the supercell approach, by mapping
("unfolding") the Berry curvature from the folded Brillouin zone of the
disordered supercell onto the normal Brillouin zone of the pristine crystal,
and then averaging over several realizations of disorder. We use this scheme to
study from first-principles the effect of sulfur vacancies on the valley Hall
conductivity of monolayer MoS2. In dirty samples the intrinsic valley Hall
conductivity receives gating-dependent corrections that are only weakly
dependent on the impurity concentration, consistent with side-jump scattering
and the unfolded Berry curvature can be interpreted as a k-space resolved
side-jump. At low impurity concentrations skew scattering dominates, leading to
a divergent valley Hall conductivity in the clean limit. The implications for
the recently-observed photoinduced anomalous Hall effect are discussed. | cond-mat_dis-nn |
Numerical Study of a Many-Body Localized System Coupled to a Bath: We use exact diagonalization to study the breakdown of many-body localization
in a strongly disordered and interacting system coupled to a thermalizing
environment. We show that the many-body level statistics cross over from
Poisson to GOE, and the localized eigenstates thermalize, with the crossover
coupling decreasing with the size of the bath in a manner consistent with the
hypothesis that an infinitesimally small coupling to a thermodynamic bath
should destroy localization of the eigenstates. However, signatures of
incomplete localization survive in spectral functions of local operators even
when the coupling to the environment is non-zero. These include a discrete
spectrum and a gap at zero frequency. Both features are washed out by line
broadening as one increases the coupling to the bath. | cond-mat_dis-nn |
Energy barriers in spin glasses: For an Ising spin glass on a hierarchical lattice, we show that the energy
barrier to be overcome during the flip of a domain of size L scales as L to the
power d-1 for all dimensions d. We do this by investigating appropriate lower
bounds to the barrier energy, which can be evaluated using an algorithm that
remains fast for large system sizes and dimensions. The asymptotic limit of
infinite dimensions is evaluated analytically. | cond-mat_dis-nn |
Fractal fluctuations at mixed-order transitions in interdependent
networks: We study the geometrical features of the order parameter's fluctuations near
the critical point of mixed-order phase transitions in randomly interdependent
spatial networks. In contrast to continuous transitions, where the structure of
the order parameter at criticality is fractal, in mixed-order transitions the
structure of the order parameter is known to be compact. Remarkably, we find
that although being compact, the fluctuations of the order parameter close to
mixed-order transitions are fractal up to a well-defined correlation length
$\xi'$, which diverges when approaching the critical threshold. We characterize
the self-similar nature of these critical fluctuations through their fractal
dimension, $d_f'=3d/4$, and correlation length exponent, $\nu'=2/d$, where $d$
is the dimension of the system. By means of percolation and magnetization, we
demonstrate that $d_f'$ and $\nu'$ are independent on the symmetry of the
underlying process for any $d$ of the underlying networks. | cond-mat_dis-nn |
The disordered-free-moment phase: a low-field disordered state in
spin-gap antiferromagnets with site dilution: Site dilution of spin-gapped antiferromagnets leads to localized free
moments, which can order antiferromagnetically in two and higher dimensions.
Here we show how a weak magnetic field drives this order-by-disorder state into
a novel disordered-free-moment phase, characterized by the formation of local
singlets between neighboring moments and by localized moments aligned
antiparallel to the field. This disordered phase is characterized by the
absence of a gap, as it is the case in a Bose glass. The associated
field-driven quantum phase transition is consistent with the universality of a
superfluid-to-Bose-glass transition. The robustness of the
disordered-free-moment phase and its prominent features, in particular a series
of pseudo-plateaus in the magnetization curve, makes it accessible and relevant
to experiments. | cond-mat_dis-nn |
Application of semidefinite programming to maximize the spectral gap
produced by node removal: The smallest positive eigenvalue of the Laplacian of a network is called the
spectral gap and characterizes various dynamics on networks. We propose
mathematical programming methods to maximize the spectral gap of a given
network by removing a fixed number of nodes. We formulate relaxed versions of
the original problem using semidefinite programming and apply them to example
networks. | cond-mat_dis-nn |
Kinetic Theory Approach to the SK Spin Glass Model with Glauber Dynamics: I present a new method to analyze Glauber dynamics of the
Sherrington-Kirkpatrick (SK) spin glass model. The method is based on ideas
used in the classical kinetic theory of fluids. I apply it to study spin
correlations in the high temperature phase ($T\ge T_c$) of the SK model at zero
external field. The zeroth order theory is equivalent to a disorder dependent
local equilibrium approximation. Its predictions agree well with computer
simulation results. The first order theory involves coupled evolution equations
for the spin correlations and the dynamic (excess) parts of the local field
distributions. It accounts qualitatively for the error made in the zeroth
approximation. | cond-mat_dis-nn |
Quantum simulation of long range $XY$ quantum spin glass with strong
area-law violation using trapped ions: Ground states of local Hamiltonians are known to obey the entanglement
entropy area law. While area law violation of a mild kind (logarithmic) is
commonly encountered, strong area-law violation (more than logarithmic) is
rare. In this paper, we study the long range quantum spin glass in one
dimension whose couplings are disordered and fall off with distance as a
power-law. We show that this system exhibits more than logarithmic area law
violation in its ground state. Strikingly this feature is found to be true even
in the short range regime in sharp contrast to the spinless long range
disordered fermionic model. This necessitates the study of large systems for
the quantum $XY$ spin glass model which is challenging since these numerical
methods depend on the validity of the area law. This situation lends itself
naturally for the exploration of a quantum simulation approach. We present a
proof-of-principle implementation of this non-trivially interacting spin model
using trapped ions and provide a detailed study of experimentally realistic
parameters. | cond-mat_dis-nn |
Slow dynamics and stress relaxation in a liquid as an elastic medium: We propose a new framework to discuss the transition from exponential
relaxation in a liquid to the regime of slow dynamics. For the purposes of
stress relaxation, we show that a liquid can be treated as an elastic medium.
We discuss that, on lowering the temperature, the feed-forward interaction
mechanism between local relaxation events becomes operative, and results in
slow relaxation. | cond-mat_dis-nn |
Low-temperature kinetics of exciton-exciton annihilation of weakly
localized one-dimensional Frenkel excitons: We present results of numerical simulations of the kinetics of
exciton-exciton annihilation of weakly localized one-dimensional Frenkel
excitons at low temperatures. We find that the kinetics is represented by two
well-distinguished components: a fast short-time decay and a very slow
long-time tail. The former arises from excitons that initially reside in states
belonging to the same localization segment of the chain, while the slow
component is caused by excitons created on different localization segments. We
show that the usual bi-molecular theory fails in the description of the
behavior found. We also present a qualitative analytical explanation of the
non-exponential behavior observed in both the short- and the long-time decay
components. | cond-mat_dis-nn |
Degree Distribution of Competition-Induced Preferential Attachment
Graphs: We introduce a family of one-dimensional geometric growth models, constructed
iteratively by locally optimizing the tradeoffs between two competing metrics,
and show that this family is equivalent to a family of preferential attachment
random graph models with upper cutoffs. This is the first explanation of how
preferential attachment can arise from a more basic underlying mechanism of
local competition. We rigorously determine the degree distribution for the
family of random graph models, showing that it obeys a power law up to a finite
threshold and decays exponentially above this threshold.
We also rigorously analyze a generalized version of our graph process, with
two natural parameters, one corresponding to the cutoff and the other a
``fertility'' parameter. We prove that the general model has a power-law degree
distribution up to a cutoff, and establish monotonicity of the power as a
function of the two parameters. Limiting cases of the general model include the
standard preferential attachment model without cutoff and the uniform
attachment model. | cond-mat_dis-nn |
A generation-based particle-hole density-matrix renormalization group
study of interacting quantum dots: The particle-hole version of the density-matrix renormalization-group method
(PH-DMRG) is utilized to calculate the ground-state energy of an interacting
two-dimensional quantum dot. We show that a modification of the method, termed
generation-based PH-DMRG, leads to significant improvement of the results, and
discuss its feasibility for the treatment of large systems. As another
application we calculate the addition spectrum. | cond-mat_dis-nn |
Full replica symmetry breaking in generalized mean--field spin glasses
with reflection symmetry: The analysis of the solution with full replica symmetry breaking in the
vicinity of $T_c$ of a general spin glass model with reflection symmetry is
performed. The leading term in the order parameter function expansion is
obtained. Parisi equation for the model is written. | cond-mat_dis-nn |
Instantaneous normal modes in liquids: a heterogeneous-elastic-medium
approach: The concept of vibrational density of states in glasses has been mirrored in
liquids by the instantaneous-normal-mode spectrum. While in glasses
instantaneous configurations correspond to minima of the potential-energy
hypersurface and all eigenvalues of the associated Hessian matrix are therefore
positive, in liquids this is no longer true, and modes corresponding to both
positive and negative eigenvalues exist. The instantaneous-normal-mode spectrum
has been numerically investigated in the past, and it has been demonstrated to
bring important information on the liquid dynamics. A systematic deeper
theoretical understanding is now needed. Heterogeneous-elasticity theory has
proven to be successful in explaining many details of the low-frequency
excitations in glasses, ranging from the thoroughly studied boson peak, down to
the more elusive non-phononic excitations observed in numerical simulations at
the lowest frequencies. Here we present an extension of
heterogeneous-elasticity theory to the liquid state, and show that the outcome
of the theory agrees well to the results of extensive molecular-dynamics
simulations of a model liquid at different temperatures. We show that the
spectral shape strongly depends on temperature, being symmetric at high
temperatures and becoming rather asymmetric at low temperatures, close to the
dynamical critical temperature. Most importantly, we demonstrate that the
theory naturally reproduces a surprising phenomenon, a zero-energy spectral
singularity with a cusp-like character developing in the vibrational spectra
upon cooling. This feature, known from a few previous numerical studies, has
been generally overlooked in the past due to a misleading representation of the
data. We provide a thorough analysis of this issue, based on both very accurate
predictions of our theory, and computational studies of model liquid systems
with extended size. | cond-mat_dis-nn |
Condensation phenomena with distinguishable particles: We study real-space condensation phenomena in a type of classical stochastic
processes (site-particle system), such as zero-range processes and urn models.
We here study a stochastic process in the Ehrenfest class, i.e., particles in a
site are distinguishable. In terms of the statistical mechanical analogue, the
Ehrenfest class obeys the Maxwell-Boltzmann statistics. We analytically clarify
conditions for condensation phenomena in disordered cases in the Ehrenfest
class. In addition, we discuss the preferential urn model as an example of the
disordered urn model. It becomes clear that the quenched disorder property
plays an important role in the occurrence of the condensation phenomenon in the
preferential urn model. It is revealed that the preferential urn model shows
three types of condensation depending on the disorder parameters. | cond-mat_dis-nn |
Symmetry breaking between statistically equivalent, independent channels
in a few-channel chaotic scattering: We study the distribution function $P(\omega)$ of the random variable $\omega
= \tau_1/(\tau_1 + ... + \tau_N)$, where $\tau_k$'s are the partial Wigner
delay times for chaotic scattering in a disordered system with $N$ independent,
statistically equivalent channels. In this case, $\tau_k$'s are i.i.d. random
variables with a distribution $\Psi(\tau)$ characterized by a "fat" power-law
intermediate tail $\sim 1/\tau^{1 + \mu}$, truncated by an exponential (or a
log-normal) function of $\tau$. For $N = 2$ and N=3, we observe a surprisingly
rich behavior of $P(\omega)$ revealing a breakdown of the symmetry between
identical independent channels. For N=2, numerical simulations of the quasi
one-dimensional Anderson model confirm our findings. | cond-mat_dis-nn |
Magnetic and Thermodynamic Properties of the Collective Paramagnet-Spin
Liquid Pyrochlore Tb2Ti2O7: In a recent letter [Phys. Rev. Lett. {\bf 82}, 1012 (1999)] it was found that
the Tb$^{3+}$ magnetic moments in the Tb$_2$Ti$_2$O$_7$ pyrochlore lattice of
corner-sharing tetrahedra remain in a {\it collective paramagnetic} state down
to 70mK. In this paper we present results from d.c. magnetic susceptibility,
specific heat data, inelastic neutron scattering measurements, and crystal
field calculations that strongly suggest that (1) the Tb$^{3+}$ ions in
Tb$_2$Ti$_2$O$_7$ possess a moment of approximatively 5$\mu_{\rm B}$, and (2)
the ground state $g-$tensor is extremely anisotropic below a temperature of
$O(10^0)$K, with Ising-like Tb$^{3+}$ magnetic moments confined to point along
a local cubic $<111>$ diagonal (e.g. towards the middle of the tetrahedron).
Such a very large easy-axis Ising like anisotropy along a $<111>$ direction
dramatically reduces the frustration otherwise present in a Heisenberg
pyrochlore antiferromagnet. The results presented herein underpin the
conceptual difficulty in understanding the microscopic mechanism(s) responsible
for Tb$_2$Ti$_2$O$_7$ failing to develop long-range order at a temperature of
the order of the paramagnetic Curie-Weiss temperature $\theta_{\rm CW} \approx
-10^1$K. We suggest that dipolar interactions and extra perturbative exchange
coupling(s)beyond nearest-neighbors may be responsible for the lack of ordering
of Tb$_2$Ti$_2$O$_7$. | cond-mat_dis-nn |
Response to a local quench of a system near many body localization
transition: We consider a one dimensional spin $1/2$ chain with Heisenberg interaction in
a disordered parallel magnetic field. This system is known to exhibit the many
body localization (MBL) transition at critical strength of disorder. We analyze
the response of the chain when additional perpendicular magnetic field is
applied to an individual spin and propose a method for accurate determination
of the mobility edge via local spin measurements. We further demonstrate that
the exponential decrease of the spin response with the distance between
perturbed spin and measured spin can be used to characterize the localization
length in the MBL phase. | cond-mat_dis-nn |
Approximate ground states of the random-field Potts model from graph
cuts: While the ground-state problem for the random-field Ising model is
polynomial, and can be solved using a number of well-known algorithms for
maximum flow or graph cut, the analogue random-field Potts model corresponds to
a multi-terminal flow problem that is known to be NP hard. Hence an efficient
exact algorithm is very unlikely to exist. As we show here, it is nevertheless
possible to use an embedding of binary degrees of freedom into the Potts spins
in combination with graph-cut methods to solve the corresponding ground-state
problem approximately in polynomial time. We benchmark this heuristic algorithm
using a set of quasi-exact ground states found for small systems from long
parallel tempering runs. For not too large number $q$ of Potts states, the
method based on graph cuts finds the same solutions in a fraction of the time.
We employ the new technique to analyze the breakup length of the random-field
Potts model in two dimensions. | cond-mat_dis-nn |
$T \to 0$ mean-field population dynamics approach for the random
3-satisfiability problem: During the past decade, phase-transition phenomena in the random
3-satisfiability (3-SAT) problem has been intensively studied by statistical
physics methods. In this work, we study the random 3-SAT problem by the
mean-field first-step replica-symmetry-broken cavity theory at the limit of
temperature $T\to 0$. The reweighting parameter $y$ of the cavity theory is
allowed to approach infinity together with the inverse temperature $\beta$ with
fixed ratio $r=y / \beta$. Focusing on the the system's space of satisfiable
configurations, we carry out extensive population dynamics simulations using
the technique of importance sampling and we obtain the entropy density $s(r)$
and complexity $\Sigma(r)$ of zero-energy clusters at different $r$ values. We
demonstrate that the population dynamics may reach different fixed points with
different types of initial conditions. By knowing the trends of $s(r)$ and
$\Sigma(r)$ with $r$, we can judge whether a certain type of initial condition
is appropriate at a given $r$ value. This work complements and confirms the
results of several other very recent theoretical studies. | cond-mat_dis-nn |
Self-Consistent Quantum-Field Theory for the Characterization of Complex
Random Media by Short Laser Pulses: We present a quantum field theoretical method for the characterization of
disordered complex media with short laser pulses in an optical coherence
tomography setup (OCT). We solve this scheme of coherent transport in space and
time with weighted essentially nonoscillatory methods (WENO). WENO is
preferentially used for the determination of highly nonlinear and discontinuous
processes including interference effects and phase transitions like Anderson
localization of light. The theory determines spatiotemporal characteristics of
the scattering mean free path and the transmission cross section that are
directly measurable in time-of-flight (ToF) and pump-probe experiments. The
results are a measure of the coherence of multiple scattering photons in
passive as well as in optically soft random media. Our theoretical results of
ToF are instructive in spectral regions where material characteristics such as
the scattering mean free path and the diffusion coefficient are
methodologically almost insensitive to gain or absorption and to higher-order
nonlinear effects. Our method is applicable to OCT and other advanced
spectroscopy setups including samples of strongly scattering mono- and
polydisperse complex nano- and microresonators. | cond-mat_dis-nn |
Effects of the network structural properties on its controllability: In a recent paper, it has been suggested that the controllability of a
diffusively coupled complex network, subject to localized feedback loops at
some of its vertices, can be assessed by means of a Master Stability Function
approach, where the network controllability is defined in terms of the spectral
properties of an appropriate Laplacian matrix. Following that approach, a
comparison study is reported here among different network topologies in terms
of their controllability. The effects of heterogeneity in the degree
distribution, as well as of degree correlation and community structure, are
discussed. | cond-mat_dis-nn |
Basis Glass States: New Insights from the Potential Energy Landscape: Using the potential energy landscape formalism we show that, in the
temperature range in which the dynamics of a glass forming system is thermally
activated, there exists a unique set of "basis glass states" each of which is
confined to a single metabasin of the energy landscape of a glass forming
system. These basis glass states tile the entire configuration space of the
system, exhibit only secondary relaxation and are solid-like. Any macroscopic
state of the system (whether liquid or glass) can be represented as a
superposition of basis glass states and can be described by a probability
distribution over these states. During cooling of a liquid from a high
temperature, the probability distribution freezes at sufficiently low
temperatures describing the process of liquid to glass transition. The time
evolution of the probability distribution towards the equilibrium distribution
during subsequent aging describes the primary relaxation of a glass. | cond-mat_dis-nn |
Ground-state energy distribution of disordered many-body quantum systems: Extreme-value distributions are studied in the context of a broad range of
problems, from the equilibrium properties of low-temperature disordered systems
to the occurrence of natural disasters. Our focus here is on the ground-state
energy distribution of disordered many-body quantum systems. We derive an
analytical expression that, upon tuning a parameter, reproduces with high
accuracy the ground-state energy distribution of the systems that we consider.
For some models, it agrees with the Tracy-Widom distribution obtained from
Gaussian random matrices. They include transverse Ising models, the Sachdev-Ye
model, and a randomized version of the PXP model. For other systems, such as
Bose-Hubbard models with random couplings and the disordered spin-1/2
Heisenberg chain used to investigate many-body localization, the shapes are at
odds with the Tracy-Widom distribution. Our analytical expression captures all
of these distributions, thus playing a role to the lowest energy level similar
to that played by the Brody distribution to the bulk of the spectrum. | cond-mat_dis-nn |
Metabolism of Social System: Random Boolean Network has been used to find out regulation patterns of genes
in organism. his approach is very interesting to use in a game such as N Person
PD. Here we assume that action is influenced by input in the form of choices of
cooperate or defect he accepted from other agent or group of agents in the
system. Number of cooperators, pay off value received by each agent, and
average value of the group pay off, are observed in every state, from initial
state chosen until it reaches its state cycle attractor. In simulation
performed here, we gain information that a system with large number agents
based on action on input K equals to two, will reach equilibrium and stable
condition over strategies taken out by its agents faster than higher input,
that is K equals to three. Equilibrium reached in longer interval, yet it is
stable over strategies carried out by agents. | cond-mat_dis-nn |
The Quantum Spherical p-Spin-Glass Model: We study a quantum extension of the spherical $p$-spin-glass model using the
imaginary-time replica formalism. We solve the model numerically and we discuss
two analytical approximation schemes that capture most of the features of the
solution. The phase diagram and the physical properties of the system are
determined in two ways: by imposing the usual conditions of thermodynamic
equilibrium and by using the condition of marginal stability. In both cases,
the phase diagram consists of two qualitatively different regions. If the
transition temperature is higher than a critical value $T^{\star}$, quantum
effects are qualitatively irrelevant and the phase transition is {\it second}
order, as in the classical case. However, when quantum fluctuations depress the
transition temperature below $T^{\star}$, the transition becomes {\it first
order}. The susceptibility is discontinuous and shows hysteresis across the
first order line, a behavior reminiscent of that observed in the dipolar Ising
spin-glass LiHo$_x$Y$_{1-x}$F$_4$ in an external transverse magnetic field. We
discuss in detail the thermodynamics and the stationary dynamics of both
states. The spectrum of magnetic excitations of the equilibrium spin-glass
state is gaped, leading to an exponentially small specific heat at low
temperatures. That of the marginally stable state is gapless and its specific
heat varies linearly with temperature, as generally observed in glasses at low
temperature. We show that the properties of the marginally stable state are
closely related to those obtained in studies of the real-time dynamics of the
system weakly coupled to a quantum thermal bath. Finally, we discuss a possible
application of our results to the problem of polymers in random media. | cond-mat_dis-nn |
Adaptive Thouless--Anderson--Palmer equation for higher-order Markov
random fields: The adaptive Thouless--Anderson--Palmer (TAP) mean-field approximation is one
of the advanced mean-field approaches, and it is known as a powerful accurate
method for Markov random fields (MRFs) with quadratic interactions (pairwise
MRFs). In this study, an extension of the adaptive TAP approximation for MRFs
with many-body interactions (higher-order MRFs) is developed. We show that the
adaptive TAP equation for pairwise MRFs is derived by naive mean-field
approximation with diagonal consistency. Based on the equivalence of the
approximate equation obtained from the naive mean-field approximation with
diagonal consistency and the adaptive TAP equation in pairwise MRFs, we
formulate approximate equations for higher-order Boltzmann machines, which is
one of simplest higher-order MRFs, via the naive mean-field approximation with
diagonal consistency. | cond-mat_dis-nn |
Classical versus Quantum Structure of the Scattering Probability Matrix.
Chaotic wave-guides: The purely classical counterpart of the Scattering Probability Matrix (SPM)
$\mid S_{n,m}\mid^2$ of the quantum scattering matrix $S$ is defined for 2D
quantum waveguides for an arbitrary number of propagating modes $M$. We compare
the quantum and classical structures of $\mid S_{n,m}\mid^2$ for a waveguide
with generic Hamiltonian chaos. It is shown that even for a moderate number of
channels, knowledge of the classical structure of the SPM allows us to predict
the global structure of the quantum one and, hence, understand important
quantum transport properties of waveguides in terms of purely classical
dynamics. It is also shown that the SPM, being an intensity measure, can give
additional dynamical information to that obtained by the Poincar\`{e} maps. | cond-mat_dis-nn |
Quantum Statistical Physics of Glasses at Low Temperatures: We present a quantum statistical analysis of a microscopic mean-field model
of structural glasses at low temperatures. The model can be thought of as
arising from a random Born von Karman expansion of the full interaction
potential. The problem is reduced to a single-site theory formulated in terms
of an imaginary-time path integral using replicas to deal with the disorder. We
study the physical properties of the system in thermodynamic equilibrium and
develop both perturbative and non-perturbative methods to solve the model. The
perturbation theory is formulated as a loop expansion in terms of two-particle
irreducible diagrams, and is carried to three-loop order in the effective
action. The non-perturbative description is investigated in two ways, (i) using
a static approximation, and (ii) via Quantum Monte Carlo simulations. Results
for the Matsubara correlations at two-loop order perturbation theory are in
good agreement with those of the Quantum Monte Carlo simulations.
Characteristic low-temperature anomalies of the specific heat are reproduced,
both in the non-perturbative static approximation, and from a three-loop
perturbative evaluation of the free energy. In the latter case the result so
far relies on using Matsubara correlations at two-loop order in the three-loop
expressions for the free energy, as self-consistent Matsubara correlations at
three-loop order are still unavailable. We propose to justify this by the good
agreement of two-loop Matsubara correlations with those obtained
non-perturbatively via Quantum Monte Carlo simulations. | cond-mat_dis-nn |
Synchronization of phase oscillators on the hierarchical lattice: Synchronization of neurons forming a network with a hierarchical structure is
essential for the brain to be able to function optimally. In this paper we
study synchronization of phase oscillators on the most basic example of such a
network, namely, the hierarchical lattice. Each site of the lattice carries an
oscillator that is subject to noise. Pairs of oscillators interact with each
other at a strength that depends on their hierarchical distance, modulated by a
sequence of interaction parameters. We look at block averages of the
oscillators on successive hierarchical scales, which we think of as block
communities. In the limit as the number of oscillators per community tends to
infinity, referred to as the hierarchical mean-field limit, we find a
separation of time scales, i.e., each block community behaves like a single
oscillator evolving on its own time scale. We argue that the evolution of the
block communities is given by a renormalized mean-field noisy Kuramoto
equation, with a synchronization level that depends on the hierarchical scale
of the block community. We find three universality classes for the
synchronization levels on successive hierarchical scales, characterized in
terms of the sequence of interaction parameters.
What makes our model specifically challenging is the non-linearity of the
interaction betweenthe oscillators. The main results of our paper therefore
come in three parts: (I) a conjecture about the nature of the renormalisation
transformation connecting successive hierarchical scales; (II) a truncation
approximation that leads to a simplified renormalization transformation; (III)
a rigorous analysis of the simplified renormalization transformation. We
provide compelling arguments in support of (I) and (II), but a full
verification remains an open problem. | cond-mat_dis-nn |
An Anomalously Elastic, Intermediate Phase in Randomly Layered
Superfluids, Superconductors, and Planar Magnets: We show that layered quenched randomness in planar magnets leads to an
unusual intermediate phase between the conventional ferromagnetic
low-temperature and paramagnetic high-temperature phases. In this intermediate
phase, which is part of the Griffiths region, the spin-wave stiffness
perpendicular to the random layers displays anomalous scaling behavior, with a
continuously variable anomalous exponent, while the magnetization and the
stiffness parallel to the layers both remain finite. Analogous results hold for
superfluids and superconductors. We study the two phase transitions into the
anomalous elastic phase, and we discuss the universality of these results, and
implications of finite sample size as well as possible experiments. | cond-mat_dis-nn |
Jamming in Hierarchical Networks: We study the Biroli-Mezard model for lattice glasses on a number of
hierarchical networks. These networks combine certain lattice-like features
with a recursive structure that makes them suitable for exact renormalization
group studies and provide an alternative to the mean-field approach. In our
numerical simulations here, we first explore their equilibrium properties with
the Wang-Landau algorithm. Then, we investigate their dynamical behavior using
a grand-canonical annealing algorithm. We find that the dynamics readily falls
out of equilibrium and jams in many of our networks with certain constraints on
the neighborhood occupation imposed by the Biroli-Mezard model, even in cases
where exact results indicate that no ideal glass transition exists. But while
we find that time-scales for the jams diverge, our simulations cannot ascertain
such a divergence for a packing fraction distinctly above random close packing.
In cases where we allow hopping in our dynamical simulations, the jams on these
networks generally disappear. | cond-mat_dis-nn |
How to calculate the fractal dimension of a complex network: the box
covering algorithm: Covering a network with the minimum possible number of boxes can reveal
interesting features for the network structure, especially in terms of
self-similar or fractal characteristics. Considerable attention has been
recently devoted to this problem, with the finding that many real networks are
self-similar fractals. Here we present, compare and study in detail a number of
algorithms that we have used in previous papers towards this goal. We show that
this problem can be mapped to the well-known graph coloring problem and then we
simply can apply well-established algorithms. This seems to be the most
efficient method, but we also present two other algorithms based on burning
which provide a number of other benefits. We argue that the presented
algorithms provide a solution close to optimal and that another algorithm that
can significantly improve this result in an efficient way does not exist. We
offer to anyone that finds such a method to cover his/her expenses for a 1-week
trip to our lab in New York (details in http://jamlab.org). | cond-mat_dis-nn |
Local fluctuation dissipation relation: In this letter I show that the recently proposed local version of the
fluctuation dissipation relations follows from the general principle of
stochastic stability in a way that is very similar to the usual proof of the
fluctuation dissipation theorem for intensive quantities. Similar arguments can
be used to prove that all sites in an aging experiment stay at the same
effective temperature at the same time. | cond-mat_dis-nn |
Quantum thermostatted disordered systems and sensitivity under
compression: A one-dimensional quantum system with off diagonal disorder, consisting of a
sample of conducting regions randomly interspersed within potential barriers is
considered. Results mainly concerning the large $N$ limit are presented. In
particular, the effect of compression on the transmission coefficient is
investigated. A numerical method to simulate such a system, for a physically
relevant number of barriers, is proposed. It is shown that the disordered model
converges to the periodic case as $N$ increases, with a rate of convergence
which depends on the disorder degree. Compression always leads to a decrease of
the transmission coefficient which may be exploited to design
nano-technological sensors. Effective choices for the physical parameters to
improve the sensitivity are provided. Eventually large fluctuations and rate
functions are analysed. | cond-mat_dis-nn |
Denser glasses relax faster: a competition between rejuvenation and
aging during in-situ high pressure compression at the atomic scale: A fascinating feature of metallic glasses is their ability to explore
different configurations under mechanical deformations. This effect is usually
observed through macroscopic observables, while little is known on the
consequence of the deformation at atomic level. Using the new generation of
synchrotrons, we probe the atomic motion and structure in a metallic glass
under hydrostatic compression, from the onset of the perturbation up to a
severely-compressed state. While the structure indicates reversible
densification under compression, the dynamic is dramatically accelerated and
exhibits a hysteresis with two regimes. At low pressures, the atomic motion is
heterogeneous with avalanche-like rearrangements suggesting rejuvenation, while
under further compression, aging leads to a super-diffusive dynamics triggered
by internal stresses inherent to the glass. These results highlight the
complexity of the atomic motion in non-ergodic systems and support a theory
recently developed to describe the surprising rejuvenation and strain hardening
of metallic glasses under compression. | cond-mat_dis-nn |
Dynamical studies of the response function in a Spin Glass: Experiments on the time dependence of the response function of a Ag(11 at%Mn)
spin glass at a temperature below the zero field spin glass temperature are
used to explore the non-equilibrium nature of the spin glass phase. It is found
that the response function is only governed by the thermal history in the very
neighbourhood of the actual measurement temperature. The thermal history
outside this narrow region is irrelevant to the measured response. A result
that implies that the thermal history during cooling (cooling rate, wait times
etc.) is imprinted in the spin structure and is always retained when any higher
temperature is recovered. The observations are discussed in the light of a real
space droplet/domain phenomenology. The results also emphasise the importance
of using controlled cooling procedures to acquire interpretable and
reproducible experimental results on the non-equilibrium dynamics in spin
glasses. | cond-mat_dis-nn |
Suppression of the virtual Anderson transition in a narrow impurity band
of doped quantum well structures: Earlier we reported an observation at low temperatures of activation
conductivity with small activation energies in strongly doped uncompensated
layers of p-GaAs/AlGaAs quantum wells. We attributed it to Anderson
delocalization of electronic states in the vicinity of the maximum of the
narrow impurity band. A possibility of such delocalization at relatively small
impurity concentration is related to the small width of the impurity band
characterized by weak disorder. In this case the carriers were activated from
the "bandtail" while its presence was related to weak background compensation.
Here we study an effect of the extrinsic compensation and of the impurity
concentration on this "virtual" Anderson transition. It was shown that an
increase of compensation initially does not affect the Anderson transition,
however at strong compensations the transition is suppressed due to increase of
disorder. In its turn, an increase of the dopant concentration initially leads
to a suppression of the transition due an increase of disorder, the latter
resulting from a partial overlap of the Hubbard bands. However at larger
concentration the conductivity becomes to be metallic due to Mott transition. | cond-mat_dis-nn |
Duality, Quantum Skyrmions and the Stability of an SO(3) Two-Dimensional
Quantum Spin-Glass: Quantum topological excitations (skyrmions) are analyzed from the point of
view of their duality to spin excitations in the different phases of a
disordered two-dimensional, short-range interacting, SO(3) quantum magnetic
system of Heisenberg type. The phase diagram displays all the phases, which are
allowed by the duality relation. We study the large distance behavior of the
two-point correlation function of quantum skyrmions in each of these phases
and, out of this, extract information about the energy spectrum and
non-triviality of these excitations. The skyrmion correlators present a
power-law decay in the spin-glass(SG)-phase, indicating that these quantum
topological excitations are gapless but nontrivial in this phase. The SG phase
is dual to the AF phase, in the sense that topological and spin excitations are
respectively gapless in each of them. The Berezinskii-Kosterlitz-Thouless
mechanism guarantees the survival of the SG phase at $T \neq 0$, whereas the AF
phase is washed out to T=0 by the quantum fluctuations. Our results suggest a
new, more symmetric way of characterizing a SG-phase: one for which both the
order and disorder parameters vanish, namely $<\sigma > = 0 $, $<\mu > =0 $,
where $\sigma$ is the spin and $\mu$ is the topological excitation operators. | cond-mat_dis-nn |
Destruction of first-order phase transition in a random-field Ising
model: The phase transitions that occur in an infinite-range-interaction Ising
ferromagnet in the presence of a double-Gaussian random magnetic field are
analyzed. Such random fields are defined as a superposition of two Gaussian
distributions, presenting the same width $\sigma$. Is is argued that this
distribution is more appropriate for a theoretical description of real systems
than its simpler particular cases, i.e., the bimodal ($\sigma=0$) and the
single Gaussian distributions. It is shown that a low-temperature first-order
phase transition may be destructed for increasing values of $\sigma$, similarly
to what happens in the compound $Fe_{x}Mg_{1-x}Cl_{2}$, whose
finite-temperature first-order phase transition is presumably destructed by an
increase in the field randomness. | cond-mat_dis-nn |
The birth of geometry in exponential random graphs: Inspired by the prospect of having discretized spaces emerge from random
graphs, we construct a collection of simple and explicit exponential random
graph models that enjoy, in an appropriate parameter regime, a roughly constant
vertex degree and form very large numbers of simple polygons (triangles or
squares). The models avoid the collapse phenomena that plague naive graph
Hamiltonians based on triangle or square counts. More than that, statistically
significant numbers of other geometric primitives (small pieces of regular
lattices, cubes) emerge in our ensemble, even though they are not in any way
explicitly pre-programmed into the formulation of the graph Hamiltonian, which
only depends on properties of paths of length 2. While much of our motivation
comes from hopes to construct a graph-based theory of random geometry
(Euclidean quantum gravity), our presentation is completely self-contained
within the context of exponential random graph theory, and the range of
potential applications is considerably more broad. | cond-mat_dis-nn |
Percolation in Media with Columnar Disorder: We study a generalization of site percolation on a simple cubic lattice,
where not only single sites are removed randomly, but also entire parallel
columns of sites. We show that typical clusters near the percolation transition
are very anisotropic, with different scaling exponents for the sizes parallel
and perpendicular to the columns. Below the critical point there is a Griffiths
phase where cluster size distributions and spanning probabilities in the
direction parallel to the columns have power law tails with continuously
varying non-universal powers. This region is very similar to the Griffiths
phase in subcritical directed percolation with frozen disorder in the preferred
direction, and the proof follows essentially the same arguments as in that
case. But in contrast to directed percolation in disordered media, the number
of active ("growth") sites in a growing cluster at criticality shows a power
law, while the probability of a cluster to continue to grow shows logarithmic
behavior. | cond-mat_dis-nn |
Thermodynamic properties of extremely diluted symmetric Q-Ising neural
networks: Using the replica-symmetric mean-field theory approach the thermodynamic and
retrieval properties of extremely diluted {\it symmetric} $Q$-Ising neural
networks are studied. In particular, capacity-gain parameter and
capacity-temperature phase diagrams are derived for $Q=3, 4$ and $Q=\infty$.
The zero-temperature results are compared with those obtained from a study of
the dynamics of the model. Furthermore, the de Almeida-Thouless line is
determined. Where appropriate, the difference with other $Q$-Ising
architectures is outlined. | cond-mat_dis-nn |
Logarithmic Entanglement Lightcone in Many-Body Localized Systems: We theoretically study the response of a many-body localized system to a
local quench from a quantum information perspective. We find that the local
quench triggers entanglement growth throughout the whole system, giving rise to
a logarithmic lightcone. This saturates the modified Lieb-Robinson bound for
quantum information propagation in many-body localized systems previously
conjectured based on the existence of local integrals of motion. In addition,
near the localization-delocalization transition, we find that the final states
after the local quench exhibit volume-law entanglement. We also show that the
local quench induces a deterministic orthogonality catastrophe for highly
excited eigenstates, where the typical wave-function overlap between the pre-
and post-quench eigenstates decays {\it exponentially} with the system size. | cond-mat_dis-nn |
Local level statistics for optical and transport properties of
disordered systems at finite temperature: It is argued that the (traditional) global level statistics which determines
localization and coherent transport properties of disordered systems at zero
temperature (e.g. the Anderson model) becomes inappropriate when it comes to
incoherent transport. We define local level statistics which proves to be
relevant for finite temperature incoherent transport and optics of
one-dimensional systems (e.g. molecular aggregates, conjugated polymers, etc.). | cond-mat_dis-nn |
Microscopic picture of aging in SiO2: We investigate the aging dynamics of amorphous SiO2 via molecular dynamics
simulations of a quench from a high temperature T_i to a lower temperature T_f.
We obtain a microscopic picture of aging dynamics by analyzing single particle
trajectories, identifying jump events when a particle escapes the cage formed
by its neighbors, and by determining how these jumps depend on the waiting time
t_w, the time elapsed since the temperature quench to T_f. We find that the
only t_w-dependent microscopic quantity is the number of jumping particles per
unit time, which decreases with age. Similar to previous studies for fragile
glass formers, we show here for the strong glass former SiO2 that neither the
distribution of jump lengths nor the distribution of times spent in the cage
are t_w-dependent. We conclude that the microscopic aging dynamics is
surprisingly similar for fragile and strong glass formers. | cond-mat_dis-nn |
$T \to 0$ mean-field population dynamics approach for the random
3-satisfiability problem: During the past decade, phase-transition phenomena in the random
3-satisfiability (3-SAT) problem has been intensively studied by statistical
physics methods. In this work, we study the random 3-SAT problem by the
mean-field first-step replica-symmetry-broken cavity theory at the limit of
temperature $T\to 0$. The reweighting parameter $y$ of the cavity theory is
allowed to approach infinity together with the inverse temperature $\beta$ with
fixed ratio $r=y / \beta$. Focusing on the the system's space of satisfiable
configurations, we carry out extensive population dynamics simulations using
the technique of importance sampling and we obtain the entropy density $s(r)$
and complexity $\Sigma(r)$ of zero-energy clusters at different $r$ values. We
demonstrate that the population dynamics may reach different fixed points with
different types of initial conditions. By knowing the trends of $s(r)$ and
$\Sigma(r)$ with $r$, we can judge whether a certain type of initial condition
is appropriate at a given $r$ value. This work complements and confirms the
results of several other very recent theoretical studies. | cond-mat_dis-nn |
Euclidean random matrix theory: low-frequency non-analyticities and
Rayleigh scattering: By calculating all terms of the high-density expansion of the euclidean
random matrix theory (up to second-order in the inverse density) for the
vibrational spectrum of a topologically disordered system we show that the
low-frequency behavior of the self energy is given by $\Sigma(k,z)\propto
k^2z^{d/2}$ and not $\Sigma(k,z)\propto k^2z^{(d-2)/2}$, as claimed previously.
This implies the presence of Rayleigh scattering and long-time tails of the
velocity autocorrelation function of the analogous diffusion problem of the
form $Z(t)\propto t^{(d+2)/2}$. | cond-mat_dis-nn |
From complex to simple : hierarchical free-energy landscape renormalized
in deep neural networks: We develop a statistical mechanical approach based on the replica method to
study the design space of deep and wide neural networks constrained to meet a
large number of training data. Specifically, we analyze the configuration space
of the synaptic weights and neurons in the hidden layers in a simple
feed-forward perceptron network for two scenarios: a setting with random
inputs/outputs and a teacher-student setting. By increasing the strength of
constraints,~i.e. increasing the number of training data, successive 2nd order
glass transition (random inputs/outputs) or 2nd order crystalline transition
(teacher-student setting) take place layer-by-layer starting next to the
inputs/outputs boundaries going deeper into the bulk with the thickness of the
solid phase growing logarithmically with the data size. This implies the
typical storage capacity of the network grows exponentially fast with the
depth. In a deep enough network, the central part remains in the liquid phase.
We argue that in systems of finite width N, the weak bias field can remain in
the center and plays the role of a symmetry-breaking field that connects the
opposite sides of the system. The successive glass transitions bring about a
hierarchical free-energy landscape with ultrametricity, which evolves in space:
it is most complex close to the boundaries but becomes renormalized into
progressively simpler ones in deeper layers. These observations provide clues
to understand why deep neural networks operate efficiently. Finally, we present
some numerical simulations of learning which reveal spatially heterogeneous
glassy dynamics truncated by a finite width $N$ effect. | cond-mat_dis-nn |
Critical and resonance phenomena in neural networks: Brain rhythms contribute to every aspect of brain function. Here, we study
critical and resonance phenomena that precede the emergence of brain rhythms.
Using an analytical approach and simulations of a cortical circuit model of
neural networks with stochastic neurons in the presence of noise, we show that
spontaneous appearance of network oscillations occurs as a dynamical
(non-equilibrium) phase transition at a critical point determined by the noise
level, network structure, the balance between excitatory and inhibitory
neurons, and other parameters. We find that the relaxation time of neural
activity to a steady state, response to periodic stimuli at the frequency of
the oscillations, amplitude of damped oscillations, and stochastic fluctuations
of neural activity are dramatically increased when approaching the critical
point of the transition. | cond-mat_dis-nn |
Q-Ising neural network dynamics: a comparative review of various
architectures: This contribution reviews the parallel dynamics of Q-Ising neural networks
for various architectures: extremely diluted asymmetric, layered feedforward,
extremely diluted symmetric, and fully connected. Using a probabilistic
signal-to-noise ratio analysis, taking into account all feedback correlations,
which are strongly dependent upon these architectures the evolution of the
distribution of the local field is found. This leads to a recursive scheme
determining the complete time evolution of the order parameters of the network.
Arbitrary Q and mainly zero temperature are considered. For the asymmetrically
diluted and the layered feedforward network a closed-form solution is obtained
while for the symmetrically diluted and fully connected architecture the
feedback correlations prevent such a closed-form solution. For these symmetric
networks equilibrium fixed-point equations can be derived under certain
conditions on the noise in the system. They are the same as those obtained in a
thermodynamic replica-symmetric mean-field theory approach. | cond-mat_dis-nn |
Spin glasses in the limit of an infinite number of spin components: We consider the spin glass model in which the number of spin components, m,
is infinite. In the formulation of the problem appropriate for numerical
calculations proposed by several authors, we show that the order parameter
defined by the long-distance limit of the correlation functions is actually
zero and there is only "quasi long range order" below the transition
temperature. We also show that the spin glass transition temperature is zero in
three dimensions. | cond-mat_dis-nn |
Scaling of level statistics at the metal-insulator transition: Using the Anderson model for disordered systems the fluctuations in electron
spectra near the metal--insulator transition were numerically calculated for
lattices of sizes up to 28 x 28 x 28 sites. The results show a finite--size
scaling of both the level spacing distribution and the variance of number of
states in a given energy interval, that allows to locate the critical point and
to determine the critical exponent of the localization length. | cond-mat_dis-nn |
Fluctuation-Induced Forces in Disordered Landau-Ginzburg Model: We discuss fluctuation-induced forces in a system described by a continuous
Landau-Ginzburg model with a quenched disorder field, defined in a
$d$-dimensional slab geometry $\mathbb R^{d-1}\times[0,L]$. A series
representation for the quenched free energy in terms of the moments of the
partition function is presented. In each moment an order parameter-like
quantity can be defined, with a particular correlation length of the
fluctuations. For some specific strength of the non-thermal control parameter,
it appears a moment of the partition function where the fluctuations associated
to the order parameter-like quantity becomes long-ranged. In this situation,
these fluctuations become sensitive to the boundaries. In the Gaussian
approximation, using the spectral zeta-function method, we evaluate a
functional determinant for each moment of the partition function. The analytic
structure of each spectral zeta-function depending on the dimension of the
space for the case of Dirichlet, Neumann Laplacian and also periodic boundary
conditions is discussed in a unified way. Considering the moment of the
partition function with the largest correlation length of the fluctuations, we
evaluate the induced force between the boundaries, for Dirichlet boundary
conditions. We prove that the sign of the fluctuation-induced force for this
case depend in a non-trivial way on the strength of the non-thermal control
parameter. | cond-mat_dis-nn |
Coupling-Matrix Approach to the Chern Number Calculation in Disordered
Systems: The Chern number is often used to distinguish between different topological
phases of matter in two-dimensional electron systems. A fast and efficient
coupling-matrix method is designed to calculate the Chern number in finite
crystalline and disordered systems. To show its effectiveness, we apply the
approach to the Haldane model and the lattice Hofstadter model, the quantized
Chern numbers being correctly obtained. The disorder-induced topological phase
transition is well reproduced, when the disorder strength is increased beyond
the critical value. We expect the method to be widely applicable to the study
of topological quantum numbers. | cond-mat_dis-nn |
Quantum Hall transitions: An exact theory based on conformal restriction: We revisit the problem of the plateau transition in the integer quantum Hall
effect. Here we develop an analytical approach for this transition, based on
the theory of conformal restriction. This is a mathematical theory that was
recently developed within the context of the Schramm-Loewner evolution which
describes the stochastic geometry of fractal curves and other stochastic
geometrical fractal objects in 2D space. Observables elucidating the connection
with the plateau transition include the so-called point-contact conductances
(PCCs) between points on the boundary of the sample, described within the
language of the Chalker-Coddington network model. We show that the
disorder-averaged PCCs are characterized by classical probabilities for certain
geometric objects in the plane (pictures), occurring with positive statistical
weights, that satisfy the crucial restriction property with respect to changes
in the shape of the sample with absorbing boundaries. Upon combining this
restriction property with the expected conformal invariance at the transition
point, we employ the mathematical theory of conformal restriction measures to
relate the disorder-averaged PCCs to correlation functions of primary operators
in a conformal field theory (of central charge $c=0$). We show how this can be
used to calculate these functions in a number of geometries with various
boundary conditions. Since our results employ only the conformal restriction
property, they are equally applicable to a number of other critical disordered
electronic systems in 2D. For most of these systems, we also predict exact
values of critical exponents related to the spatial behavior of various
disorder-averaged PCCs. | cond-mat_dis-nn |
Thermodynamics of spin systems on small-world hypergraphs: We study the thermodynamic properties of spin systems on small-world
hypergraphs, obtained by superimposing sparse Poisson random graphs with p-spin
interactions onto a one-dimensional Ising chain with nearest-neighbor
interactions. We use replica-symmetric transfer-matrix techniques to derive a
set of fixed-point equations describing the relevant order parameters and free
energy, and solve them employing population dynamics. In the special case where
the number of connections per site is of the order of the system size we are
able to solve the model analytically. In the more general case where the number
of connections is finite we determine the static and dynamic
ferromagnetic-paramagnetic transitions using population dynamics. The results
are tested against Monte-Carlo simulations. | cond-mat_dis-nn |
Excited-Eigenstate Entanglement Properties of XX Spin Chains with Random
Long-Range Interactions: Quantum information theoretical measures are useful tools for characterizing
quantum dynamical phases. However, employing them to study excited states of
random spin systems is a challenging problem. Here, we report results for the
entanglement entropy (EE) scaling of excited eigenstates of random XX
antiferromagnetic spin chains with long-range (LR) interactions decaying as a
power law with distance with exponent $\alpha$. To this end, we extend the
real-space renormalization group technique for excited states (RSRG-X) to solve
this problem with LR interaction. For comparison, we perform numerical exact
diagonalization (ED) calculations. From the distribution of energy level
spacings, as obtained by ED for up to $N\sim 18$ spins, we find indications of
a delocalization transition at $\alpha_c \approx 1$ in the middle of the energy
spectrum. With RSRG-X and ED, we show that for $\alpha>\alpha^*$ the
entanglement entropy (EE) of excited eigenstates retains a logarithmic
divergence similar to the one observed for the ground state of the same model,
while for $\alpha<\alpha^*$ EE displays an algebraic growth with the subsystem
size $l$, $S_l\sim l^{\beta}$, with $0<\beta<1$. We find that $\alpha^* \approx
1$ coincides with the delocalization transition $\alpha_c$ in the middle of the
many-body spectrum. An interpretation of these results based on the structure
of the RG rules is proposed, which is due to {\it rainbow} proliferation for
very long-range interactions $\alpha\ll 1$. We also investigate the effective
temperature dependence of the EE allowing us to study the half-chain
entanglement entropy of eigenstates at different energy densities, where we
find that the crossover in EE occurs at $\alpha^* < 1$. | cond-mat_dis-nn |
Evidence for universal scaling in the spin-glass phase: We perform Monte Carlo simulations of Ising spin-glass models in three and
four dimensions, as well as of Migdal-Kadanoff spin glasses on a hierarchical
lattice. Our results show strong evidence for universal scaling in the
spin-glass phase in all three models. Not only does this allow for a clean way
to compare results obtained from different coupling distributions, it also
suggests that a so far elusive renormalization group approach within the
spin-glass phase may actually be feasible. | cond-mat_dis-nn |
Universality and Quantum Criticality in Quasiperiodic Spin Chains: Quasiperiodic systems are aperiodic but deterministic, so their critical
behavior differs from that of clean systems as well as disordered ones.
Quasiperiodic criticality was previously understood only in the special limit
where the couplings follow discrete quasiperiodic sequences. Here we consider
generic quasiperiodic modulations; we find, remarkably, that for a wide class
of spin chains, generic quasiperiodic modulations flow to discrete sequences
under a real-space renormalization group transformation. These discrete
sequences are therefore fixed points of a \emph{functional} renormalization
group. This observation allows for an asymptotically exact treatment of the
critical points. We use this approach to analyze the quasiperiodic Heisenberg,
Ising, and Potts spin chains, as well as a phenomenological model for the
quasiperiodic many-body localization transition. | cond-mat_dis-nn |
The two-star model: exact solution in the sparse regime and condensation
transition: The $2$-star model is the simplest exponential random graph model that
displays complex behavior, such as degeneracy and phase transition. Despite its
importance, this model has been solved only in the regime of dense
connectivity. In this work we solve the model in the finite connectivity
regime, far more prevalent in real world networks. We show that the model
undergoes a condensation transition from a liquid to a condensate phase along
the critical line corresponding, in the ensemble parameters space, to the
Erd\"os-R\'enyi graphs. In the fluid phase the model can produce graphs with a
narrow degree statistics, ranging from regular to Erd\"os-R\'enyi graphs, while
in the condensed phase, the "excess" degree heterogeneity condenses on a single
site with degree $\sim\sqrt{N}$. This shows the unsuitability of the two-star
model, in its standard definition, to produce arbitrary finitely connected
graphs with degree heterogeneity higher than Erd\"os-R\'enyi graphs and
suggests that non-pathological variants of this model may be attained by
softening the global constraint on the two-stars, while keeping the number of
links hardly constrained. | cond-mat_dis-nn |
Strong magnetoresistance of disordered graphene: We study theoretically magnetoresistance (MR) of graphene with different
types of disorder. For short-range disorder, the key parameter determining
magnetotransport properties---a product of the cyclotron frequency and
scattering time---depends in graphene not only on magnetic field $H$ but also
on the electron energy $\varepsilon$. As a result, a strong, square-root in
$H$, MR arises already within the Drude-Boltzmann approach. The MR is
particularly pronounced near the Dirac point. Furthermore, for the same reason,
"quantum" (separated Landau levels) and "classical" (overlapping Landau levels)
regimes may coexist in the same sample at fixed $H.$ We calculate the
conductivity tensor within the self-consistent Born approximation for the case
of relatively high temperature, when Shubnikov-de Haas oscillations are
suppressed by thermal averaging. We predict a square-root MR both at very low
and at very high $H:$ $[\varrho_{xx}(H)-\varrho_{xx}(0)]/\varrho_{xx}(0)\approx
C \sqrt{H},$ where $C$ is a temperature-dependent factor, different in the low-
and strong-field limits and containing both "quantum" and "classical"
contributions. We also find a nonmonotonic dependence of the Hall coefficient
both on magnetic field and on the electron concentration. In the case of
screened charged impurities, we predict a strong temperature-independent MR
near the Dirac point. Further, we discuss the competition between disorder- and
collision-dominated mechanisms of the MR. In particular, we find that the
square-root MR is always established for graphene with charged impurities in a
generic gated setup at low temperature. | cond-mat_dis-nn |
Crackling Noise and Avalanches: Scaling, Critical Phenomena, and the
Renormalization Group: In the past two decades or so, we have learned how to understand crackling
noise in a wide variety of systems. We review here the basic ideas and methods
we use to understand crackling noise - critical phenomena, universality, the
renormalization group, power laws, and universal scaling functions. These
methods and tools were originally developed to understand continuous phase
transitions in thermal and disordered systems, and we also introduce these more
traditional applications as illustrations of the basic ideas and phenomena. | cond-mat_dis-nn |
Monte Carlo studies of quantum and classical annealing on a double-well: We present results for a variety of Monte Carlo annealing approaches, both
classical and quantum, benchmarked against one another for the textbook
optimization exercise of a simple one-dimensional double-well. In classical
(thermal) annealing, the dependence upon the move chosen in a Metropolis scheme
is studied and correlated with the spectrum of the associated Markov transition
matrix. In quantum annealing, the Path-Integral Monte Carlo approach is found
to yield non-trivial sampling difficulties associated with the tunneling
between the two wells. The choice of fictitious quantum kinetic energy is also
addressed. We find that a ``relativistic'' kinetic energy form, leading to a
higher probability of long real space jumps, can be considerably more effective
than the standard one. | cond-mat_dis-nn |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.