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Optical computation of a spin glass dynamics with tunable complexity: Spin Glasses (SG) are paradigmatic models for physical, computer science,
biological and social systems. The problem of studying the dynamics for SG
models is NP hard, i.e., no algorithm solves it in polynomial time. Here we
implement the optical simulation of a SG, exploiting the N segments of a
wavefront shaping device to play the role of the spin variables, combining the
interference at downstream of a scattering material to implement the random
couplings between the spins (the J ij matrix) and measuring the light intensity
on a number P of targets to retrieve the energy of the system. By implementing
a plain Metropolis algorithm, we are able to simulate the spin model dynamics,
while the degree of complexity of the potential energy landscape and the region
of phase diagram explored is user-defined acting on the ratio the P/N = \alpha.
We study experimentally, numerically and analytically this peculiar system
displaying a paramagnetic, a ferromagnetic and a SG phase, and we demonstrate
that the transition temperature T g to the glassy phase from the paramagnetic
phase grows with \alpha. With respect to standard in silico approach, in the
optical SG interaction terms are realized simultaneously when the independent
light rays interferes at the target screen, enabling inherently parallel
measurements of the energy, rather than computations scaling with N as in
purely in silico simulations. | cond-mat_dis-nn |
Eigenvalue spectra of large correlated random matrices: Using the diagrammatic method, we derive a set of self-consistent equations
that describe eigenvalue distributions of large correlated asymmetric random
matrices. The matrix elements can have different variances and be correlated
with each other. The analytical results are confirmed by numerical simulations.
The results have implications for the dynamics of neural and other biological
networks where plasticity induces correlations in the connection strengths
within the network. We find that the presence of correlations can have a major
impact on network stability. | cond-mat_dis-nn |
Absence of a structural glass phase in a monoatomic model liquid
predicted to undergo an ideal glass transition: We study numerically a monodisperse model of interacting classical particles
predicted to exhibit a static liquid-glass transition. Using a dynamical Monte
Carlo method we show that the model does not freeze into a glassy phase at low
temperatures. Instead, depending on the choice of the hard-core radius for the
particles the system either collapses trivially or a polycrystalline hexagonal
structure emerges. | cond-mat_dis-nn |
Localization of Electronic Wave Functions on Quasiperiodic Lattices: We study electronic eigenstates on quasiperiodic lattices using a
tight-binding Hamiltonian in the vertex model. In particular, the
two-dimensional Penrose tiling and the three-dimensional icosahedral
Ammann-Kramer tiling are considered. Our main interest concerns the decay form
and the self-similarity of the electronic wave functions, which we compute
numerically for periodic approximants of the perfect quasiperiodic structure.
In order to investigate the suggested power-law localization of states, we
calculate their participation numbers and structural entropy. We also perform a
multifractal analysis of the eigenstates by standard box-counting methods. Our
results indicate a rather different behaviour of the two- and the
three-dimensional systems. Whereas the eigenstates on the Penrose tiling
typically show power-law localization, this was not observed for the
icosahedral tiling. | cond-mat_dis-nn |
Phase ordering on small-world networks with nearest-neighbor edges: We investigate global phase coherence in a system of coupled oscillators on a
small-world networks constructed from a ring with nearest-neighbor edges. The
effects of both thermal noise and quenched randomness on phase ordering are
examined and compared with the global coherence in the corresponding \xy model
without quenched randomness. It is found that in the appropriate regime phase
ordering emerges at finite temperatures, even for a tiny fraction of shortcuts.
Nature of the phase transition is also discussed. | cond-mat_dis-nn |
Influence of boundary conditions on level statistics and eigenstates at
the metal insulator transition: We investigate the influence of the boundary conditions on the scale
invariant critical level statistics at the metal insulator transition of
disordered three-dimensional orthogonal and two-dimensional unitary and
symplectic tight-binding models. The distribution of the spacings between
consecutive eigenvalues is calculated numerically and shown to be different for
periodic and Dirichlet boundary conditions whereas the critical disorder
remains unchanged. The peculiar correlations of the corresponding critical
eigenstates leading to anomalous diffusion seem not to be affected by the
change of the boundary conditions. | cond-mat_dis-nn |
Scaling Theory of Few-Particle Delocalization: We develop a scaling theory of interaction-induced delocalization of
few-particle states in disordered quantum systems. In the absence of
interactions, all single-particle states are localized in $d<3$, while in $d
\geq 3$ there is a critical disorder below which states are delocalized. We
hypothesize that such a delocalization transition occurs for $n$-particle bound
states in $d$ dimensions when $d+n\geq 4$. Exact calculations of
disorder-averaged $n$-particle Greens functions support our hypothesis. In
particular, we show that $3$-particle states in $d=1$ with nearest-neighbor
repulsion will delocalize with $W_c \approx 1.4t$ and with localization length
critical exponent $\nu = 1.5 \pm 0.3$. The delocalization transition can be
understood by means of a mapping onto a non-interacting problem with symplectic
symmetry. We discuss the importance of this result for many-body
delocalization, and how few-body delocalization can be probed in cold atom
experiments. | cond-mat_dis-nn |
Water adsorption on amorphous silica surfaces: A Car-Parrinello
simulation study: A combination of classical molecular dynamics (MD) and ab initio
Car-Parrinello molecular dynamics (CPMD) simulations is used to investigate the
adsorption of water on a free amorphous silica surface. From the classical MD
SiO_2 configurations with a free surface are generated which are then used as
starting configurations for the CPMD.We study the reaction of a water molecule
with a two-membered ring at the temperature T=300K. We show that the result of
this reaction is the formation of two silanol groups on the surface. The
activation energy of the reaction is estimated and it is shown that the
reaction is exothermic. | cond-mat_dis-nn |
A mesoscopic approach to subcritical fatigue crack growth: We investigate a model for fatigue crack growth in which damage accumulation
is assumed to follow a power law of the local stress amplitude, a form which
can be generically justified on the grounds of the approximately self-similar
aspect of microcrack distributions. Our aim is to determine the relation
between model ingredients and the Paris exponent governing subcritical
crack-growth dynamics at the macroscopic scale, starting from a single small
notch propagating along a fixed line. By a series of analytical and numerical
calculations, we show that, in the absence of disorder, there is a critical
damage-accumulation exponent $\gamma$, namely $\gamma_c=2$, separating two
distinct regimes of behavior for the Paris exponent $m$. For $\gamma>\gamma_c$,
the Paris exponent is shown to assume the value $m=\gamma$, a result which
proves robust against the separate introduction of various modifying
ingredients. Explicitly, we deal here with (i) the requirement of a minimum
stress for damage to occur; (ii) the presence of disorder in local damage
thresholds; (iii) the possibility of crack healing. On the other hand, in the
regime $\gamma<\gamma_c$ the Paris exponent is seen to be sensitive to the
different ingredients added to the model, with rapid healing or a high minimum
stress for damage leading to $m=2$ for all $\gamma<\gamma_c$, in contrast with
the linear dependence $m=6-2\gamma$ observed for very long characteristic
healing times in the absence of a minimum stress for damage. Upon the
introduction of disorder on the local fatigue thresholds, which leads to the
possible appearance of multiple cracks along the propagation line, the Paris
exponent tends to $m\approx 4$ for $\gamma\lesssim 2$, while retaining the
behavior $m=\gamma$ for $\gamma\gtrsim 4$. | cond-mat_dis-nn |
Kinetic-growth self-avoiding walks on small-world networks: Kinetically-grown self-avoiding walks have been studied on Watts-Strogatz
small-world networks, rewired from a two-dimensional square lattice. The
maximum length L of this kind of walks is limited in regular lattices by an
attrition effect, which gives finite values for its mean value < L >. For
random networks, this mean attrition length < L > scales as a power of the
network size, and diverges in the thermodynamic limit (large system size N).
For small-world networks, we find a behavior that interpolates between those
corresponding to regular lattices and randon networks, for rewiring probability
p ranging from 0 to 1. For p < 1, the mean self-intersection and attrition
length of kinetically-grown walks are finite. For p = 1, < L > grows with
system size as N^{1/2}, diverging in the thermodynamic limit. In this limit and
close to p = 1, the mean attrition length diverges as (1-p)^{-4}. Results of
approximate probabilistic calculations agree well with those derived from
numerical simulations. | cond-mat_dis-nn |
Critical behavior of the 2D Ising model with long-range correlated
disorder: We study critical behavior of the diluted 2D Ising model in the presence of
disorder correlations which decay algebraically with distance as $\sim r^{-a}$.
Mapping the problem onto 2D Dirac fermions with correlated disorder we
calculate the critical properties using renormalization group up to two-loop
order. We show that beside the Gaussian fixed point the flow equations have a
non trivial fixed point which is stable for $0.995<a<2$ and is characterized by
the correlation length exponent $\nu= 2/a + O((2-a)^3)$. Using bosonization, we
also calculate the averaged square of the spin-spin correlation function and
find the corresponding critical exponent $\eta_2=1/2-(2-a)/4+O((2-a)^2)$. | cond-mat_dis-nn |
Possible origin of $β$-relaxation in amorphous metal alloys from
atomic-mass differences of the constituents: We employ an atomic-scale theory within the framework of nonaffine lattice
dynamics to uncover the origin of the Johari-Goldstein (JG) $\beta$-relaxation
in metallic glasses (MGs). Combining simulation and experimental data with our
theoretical approach, we reveal that the large mass asymmetry between the
elements in a La$_{60}$Ni$_{15}$Al$_{25}$ MG leads to a clear separation in the
respective relaxation time scales, giving strong evidence that JG relaxation is
controlled by the lightest atomic species present. Moreover, we show that only
qualitative features of the vibrational density of states determine the overall
observed mechanical response of the glass, paving the way for a possible
unified theory of secondary relaxations in glasses. | cond-mat_dis-nn |
Linear-scale simulations of quench dynamics: The accurate description and robust computational modeling of the
nonequilibrium properties of quantum systems remain a challenge in condensed
matter physics. In this work, we develop a linear-scale computational
simulation technique for the non-equilibrium dynamics of quantum quench
systems. In particular, we report a polynomial-expansion of the Loschmidt echo
to describe the dynamical quantum phase transitions of noninteracting quantum
quench systems. An expansion-based method allows us to efficiently compute the
Loschmidt echo for infinitely large systems without diagonalizing the system
Hamiltonian. To demonstrate its utility, we highlight quantum quenching
dynamics under tight-binding quasicrystals and disordered lattices in one
spatial dimension. In addition, the role of the wave vector on the quench
dynamics under lattice models is addressed. We observe wave vector-independent
dynamical phase transitions in self-dual localization models. | cond-mat_dis-nn |
Dielectric spectroscopy on aging glasses: In the present work, we provide further evidence for the applicability of a
modified stretched-exponential behavior, proposed recently for the description
of aging-time dependent data below the glass temperature [P. Lunkenheimer et
al., Phys. Rev. Lett. 95 (2005) 055702]. We analyze time-dependent dielectric
loss data in a variety of aging glasses, including new data on Salol and
propylene carbonate, using a conventional stretched exponential and the newly
proposed approach. Also the scaling of aging data obtained at different
measuring frequencies, which was predicted on the basis of the new approach, is
checked for its validity. | cond-mat_dis-nn |
Red shift of the superconductivity cavity resonance in Josephson
junction qubits as a direct signature of TLS population inversion: Quantum two-level systems (TLSs) limit the performance of superconducting
qubits and superconducting and optomechanical resonators breaking down the
coherence and absorbing the energy of oscillations. TLS absorption can be
suppressed or even switched to the gain regime by inverting TLS populations.
Here we theoretically explore the regime where the full inversion of TLS
populations is attained at energies below a pump field quantization energy by
simultaneously applying the pump field and the time varying bias. This regime
is attained changing the bias sufficiently slowly to fully invert TLS
populations when their energies cross resonance with the pump field and
sufficiently fast to avoid TLS relaxation between two resonance crossing
events. This population inversion is accompanied by a significant red shift of
cavity resonance due to quantum level repulsion. The red-shift in frequency
serves as a signature of the population inversion, as its re-entrant behavior
as function of bias sweep rate and of the magnitude of the pump field allows
the determination of the TLSs dipole moment and relaxation time. The predicted
behavior is qualitatively consistent with the recent experimental observations
in Al superconducting resonators. | cond-mat_dis-nn |
Comparing extremal and thermal Explorations of Energy Landscapes: Using a non-thermal local search, called Extremal Optimization (EO), in
conjunction with a recently developed scheme for classifying the valley
structure of complex systems, we analyze a short-range spin glass. In
comparison with earlier studies using a thermal algorithm with detailed
balance, we determine which features of the landscape are algorithm dependent
and which are inherently geometrical. Apparently a characteristic for any local
search in complex energy landscapes, the time series of successive energy
records found by EO also is characterized approximately by a log-Poisson
statistics. Differences in the results provide additional insights into the
performance of EO. In contrast with a thermal search, the extremal search
visits dramatically higher energies while returning to more widely separated
low-energy configurations. Two important properties of the energy landscape are
independent of either algorithm: first, to find lower energy records,
progressively higher energy barriers need to be overcome. Second, the Hamming
distance between two consecutive low-energy records is linearly related to the
height of the intervening barrier. | cond-mat_dis-nn |
Ground State and Spin Glass Phase of the Large N Infinite Range Spin
Glass Via Supersymmetry: The large N infinite range spin glass is considered, in particular the number
of spin components k needed to form the ground state and the sample-to-sample
fluctuations in the Lagrange multiplier field on each site. The physical
significance of k for the correlation functions is discussed. The difference
between the large N and spherical spin glass is emphasized; a slight difference
between the average Lagrange multiplier of the large N and spherical spin
glasses is derived, leading to a slight increase in the energy of the ground
state compared to the naive expectation. Further, there is a change in the low
energy density of excitations in the large N system. A form of level repulsion,
similar to that found in random matrix theory, is found to exist in this
system, surviving interactions. Even though the system is an interacting one, a
supersymmetric formalism is developed to deal with the problem of averaging
over disorder. | cond-mat_dis-nn |
Reentrant and Forward Phase Diagrams of the Anisotropic
Three-Dimensional Ising Spin Glass: The spatially uniaxially anisotropic d=3 Ising spin glass is solved exactly
on a hierarchical lattice. Five different ordered phases, namely ferromagnetic,
columnar, layered, antiferromagnetic, and spin-glass phases, are found in the
global phase diagram. The spin-glass phase is more extensive when randomness is
introduced within the planes than when it is introduced in lines along one
direction. Phase diagram cross-sections, with no Nishimori symmetry, with
Nishimori symmetry lines, or entirely imbedded into Nishimori symmetry, are
studied. The boundary between the ferromagnetic and spin-glass phases can be
either reentrant or forward, that is either receding from or penetrating into
the spin-glass phase, as temperature is lowered. However, this boundary is
always reentrant when the multicritical point terminating it is on the
Nishimori symmetry line. | cond-mat_dis-nn |
The Gardner transition in finite dimensions: Recent works on hard spheres in the limit of infinite dimensions revealed
that glass states, envisioned as meta-basins in configuration space, can break
up in a multitude of separate basins at low enough temperature or high enough
pressure, leading to the emergence of new kinds of soft-modes and unusual
properties. In this paper we study by perturbative renormalisation group
techniques the critical properties of this transition, which has been
discovered in disordered mean-field models in the '80s. We find that the upper
critical dimension $d_u$ above which mean-field results hold is strictly larger
than six and apparently non-universal, i.e. system dependent. Below $d_u$, we
do not find any perturbative attractive fixed point (except for a tiny region
of the 1RSB breaking parameter), thus showing that the transition in three
dimensions either is governed by a non-perturbative fixed point unrelated to
the Gaussian mean-field one or becomes first order or does not exist. We also
discuss possible relationships with the behavior of spin glasses in a field. | cond-mat_dis-nn |
Crossover from the chiral to the standard universality classes in the
conductance of a quantum wire with random hopping only: The conductance of a quantum wire with off-diagonal disorder that preserves a
sublattice symmetry (the random hopping problem with chiral symmetry) is
considered. Transport at the band center is anomalous relative to the standard
problem of Anderson localization both in the diffusive and localized regimes.
In the diffusive regime, there is no weak-localization correction to the
conductance and universal conductance fluctuations are twice as large as in the
standard cases. Exponential localization occurs only for an even number of
transmission channels in which case the localization length does not depend on
whether time-reversal and spin rotation symmetry are present or not. For an odd
number of channels the conductance decays algebraically. Upon moving away from
the band center transport characteristics undergo a crossover to those of the
standard universality classes of Anderson localization. This crossover is
calculated in the diffusive regime. | cond-mat_dis-nn |
Universal frequency-dependent ac conductivity of conducting polymer
networks: A model based on the aspect of the distribution of the length of conduction
paths accessible for electric charge flow reproduces the universal power-law
dispersive ac conductivity observed in polymer networks and, generally, in
disordered matter. Power exponents larger than unity observed in some cases are
physically acceptable within this model. A saturation high frequency region is
also predicted, in agreement with experimental results. There does not exist a
universal fractional power law (and is useless searching for a unique common
critical exponent), but a qualitative universal behavior of the ac conductivity
in disordered media. | cond-mat_dis-nn |
Revisiting the slow dynamics of a silica melt using Monte Carlo
simulations: We implement a standard Monte Carlo algorithm to study the slow, equilibrium
dynamics of a silica melt in a wide temperature regime, from 6100 K down to
2750 K. We find that the average dynamical behaviour of the system is in
quantitative agreement with results obtained from molecular dynamics
simulations, at least in the long-time regime corresponding to the
alpha-relaxation. By contrast, the strong thermal vibrations related to the
Boson peak present at short times in molecular dynamics are efficiently
suppressed by the Monte Carlo algorithm. This allows us to reconsider silica
dynamics in the context of mode-coupling theory, because several shortcomings
of the theory were previously attributed to thermal vibrations. A mode-coupling
theory analysis of our data is qualitatively correct, but quantitative tests of
the theory fail, raising doubts about the very existence of an avoided
singularity in this system. We discuss the emergence of dynamic heterogeneity
and report detailed measurements of a decoupling between translational
diffusion and structural relaxation, and of a growing four-point dynamic
susceptibility. Dynamic heterogeneity appears to be less pronounced than in
more fragile glass-forming models, but not of a qualitatively different nature. | cond-mat_dis-nn |
Nontrivial critical behavior of the free energy in the two-dimensional
Ising spin glass with bimodal interactions: A detailed analysis of Monte Carlo data on the two-dimensional Ising spin
glass with bimodal interactions shows that the free energy of the model has a
nontrivial scaling. In particular, we show by studying the correlation length
that much larger system sizes and lower temperatures are required to see the
true critical behavior of the model in the thermodynamic limit. Our results
agree with data by Lukic et al. in that the degenerate ground state is
separated from the first excited state by an energy gap of 2J. | cond-mat_dis-nn |
Variant Monte Carlo algorithm for driven elastic strings in random media: We discuss the non-local Variant Monte Carlo algorithm which has been
successfully employed in the study of driven elastic strings in disordered
media at the depinning threshold. Here we prove two theorems, which establish
that the algorithm satisfies the crucial no-passing rule and that, after some
initial time, the string exclusively moves forward. The Variant Monte Carlo
algorithm overcomes the shortcomings of local methods, as we show by analyzing
the depinning threshold of a single-pin problem. | cond-mat_dis-nn |
Spike-Train Responses of a Pair of Hodgkin-Huxley Neurons with
Time-Delayed Couplings: Model calculations have been performed on the spike-train response of a pair
of Hodgkin-Huxley (HH) neurons coupled by recurrent excitatory-excitatory
couplings with time delay. The coupled, excitable HH neurons are assumed to
receive the two kinds of spike-train inputs: the transient input consisting of
$M$ impulses for the finite duration ($M$: integer) and the sequential input
with the constant interspike interval (ISI). The distribution of the output ISI
$T_{\rm o}$ shows a rich of variety depending on the coupling strength and the
time delay. The comparison is made between the dependence of the output ISI for
the transient inputs and that for the sequential inputs. | cond-mat_dis-nn |
Mechanical Spectroscopy on Volcanic Glasses: Mechanical relaxation behaviour of various natural volcanic glasses have been
investigated in the temperature range RT-1200K using special low frequency
flexure (f~0.63Hz) pendulum experiments. The rheological properties complex
Young's modulus M* and internal friction 1/Q have been studied from a pure
elastic solid at room temperature to pure viscous melt at log(eta[Pas])=8.
Several relaxation processes are assumed to act: the primary alpha-relaxation
(viscoelastic process, E_a=(344...554)kJ/mol) above the glass transition
temperature T_g=(935...1105)K and secondary anelastic beta', beta and
gamma-relaxation processes below T_g. With a simple fractional Maxwell model
with asymmetrical relaxation time distribution, phenomenological the mechanical
relaxation behaviour, is described. This establish a basis of realistic
concepts for modelling of volcanic or magmatic processes. | cond-mat_dis-nn |
Weakly driven anomalous diffusion in non-ergodic regime: an analytical
solution: We derive the probability density of a diffusion process generated by
nonergodic velocity fluctuations in presence of a weak potential, using the
Liouville equation approach. The velocity of the diffusing particle undergoes
dichotomic fluctuations with a given distribution $\psi(\tau)$ of residence
times in each velocity state. We obtain analytical solutions for the diffusion
process in a generic external potential and for a generic statistics of
residence times, including the non-ergodic regime in which the mean residence
time diverges. We show that these analytical solutions are in agreement with
numerical simulations. | cond-mat_dis-nn |
Enhancement of the Magnetocaloric Effect in Geometrically Frustrated
Cluster Spin Glass Systems: In this work, we theoretically demonstrate that a strong enhancement of the
Magnetocaloric Effect is achieved in geometrically frustrated cluster
spin-glass systems just above the freezing temperature. We consider a network
of clusters interacting randomly which have triangular structure composed of
Ising spins interacting antiferromagnetically. The intercluster disorder
problem is treated using a cluster spin glass mean-field theory, which allows
exact solution of the disordered problem. The intracluster part can be solved
using exact enumeration. The coupling between the inter and intracluster
problem incorporates the interplay between effects coming from geometric
frustration and disorder. As a result, it is shown that there is the onset of
cluster spin glass phase even with very weak disorder. Remarkably, it is
exactly within a range of very weak disorder and small magnetic field that is
observed the strongest isothermal release of entropy. | cond-mat_dis-nn |
Influence of synaptic interaction on firing synchronization and spike
death in excitatory neuronal networks: We investigated the influence of efficacy of synaptic interaction on firing
synchronization in excitatory neuronal networks. We found spike death
phenomena, namely, the state of neurons transits from limit cycle to fixed
point or transient state. The phenomena occur under the perturbation of
excitatory synaptic interaction that has a high efficacy. We showed that the
decrease of synaptic current results in spike death through depressing the
feedback of sodium ionic current. In the networks with spike death property the
degree of synchronization is lower and unsensitive to the heterogeneity of
neurons. The mechanism of the influence is that the transition of neuron state
disrupts the adjustment of the rhythm of neuron oscillation and prevents
further increase of firing synchronization. | cond-mat_dis-nn |
Effect of dilution in asymmetric recurrent neural networks: We study with numerical simulation the possible limit behaviors of
synchronous discrete-time deterministic recurrent neural networks composed of N
binary neurons as a function of a network's level of dilution and asymmetry.
The network dilution measures the fraction of neuron couples that are
connected, and the network asymmetry measures to what extent the underlying
connectivity matrix is asymmetric. For each given neural network, we study the
dynamical evolution of all the different initial conditions, thus
characterizing the full dynamical landscape without imposing any learning rule.
Because of the deterministic dynamics, each trajectory converges to an
attractor, that can be either a fixed point or a limit cycle. These attractors
form the set of all the possible limit behaviors of the neural network. For
each network, we then determine the convergence times, the limit cycles'
length, the number of attractors, and the sizes of the attractors' basin. We
show that there are two network structures that maximize the number of possible
limit behaviors. The first optimal network structure is fully-connected and
symmetric. On the contrary, the second optimal network structure is highly
sparse and asymmetric. The latter optimal is similar to what observed in
different biological neuronal circuits. These observations lead us to
hypothesize that independently from any given learning model, an efficient and
effective biologic network that stores a number of limit behaviors close to its
maximum capacity tends to develop a connectivity structure similar to one of
the optimal networks we found. | cond-mat_dis-nn |
Heterogeneous diffusion, viscosity and the Stokes Einstein relation in
binary liquids: We investigate the origin of the breakdown of the Stokes-Einstein relation
(SER) between diffusivity and viscosity in undercooled melts. A binary
Lennard-Jones system, as a model for a metallic melt, is studied by molecular
dynamics. A weak breakdown at high temperatures can be understood from the
collectivization of motion, seen in the isotope effect. The strong breakdown at
lower temperatures is connected to an increase in dynamic heterogeneity. On
relevant timescales some particles diffuse much faster than the average or than
predicted by the SER. The van-Hove self correlation function allows to
unambiguously identify slow particles. Their diffusivity is even less than
predicted by the SER. The time-span of these particles being slow particles,
before their first conversion to be a fast one, is larger than the decay time
of the stress correlation. The contribution of the slow particles to the
viscosity rises rapidly upon cooling. Not only the diffusion but also the
viscosity shows a dynamically heterogeneous scenario. We can define a "slow"
viscosity. The SER is recovered as relation between slow diffusivity and slow
viscosity. | cond-mat_dis-nn |
Multitasking network with fast noise: We consider the multitasking associative network in the low-storage limit and
we study its phase diagram with respect to the noise level $T$ and the degree
$d$ of dilution in pattern entries. We find that the system is characterized by
a rich variety of stable states, among which pure states, parallel retrieval
states, hierarchically organized states and symmetric mixtures (remarkably,
both even and odd), whose complexity increases as the number of patterns $P$
grows. The analysis is performed both analytically and numerically: Exploiting
techniques based on partial differential equations, allows us to get the
self-consistencies for the order parameters. Such self-consistence equations
are then solved and the solutions are further checked through stability theory
to catalog their organizations into the phase diagram, which is completely
outlined at the end. This is a further step toward the understanding of
spontaneous parallel processing in associative networks. | cond-mat_dis-nn |
Preferential attachment with information filtering - node degree
probability distribution properties: A network growth mechanism based on a two-step preferential rule is
investigated as a model of network growth in which no global knowledge of the
network is required. In the first filtering step a subset of fixed size $m$ of
existing nodes is randomly chosen. In the second step the preferential rule of
attachment is applied to the chosen subset. The characteristics of thus formed
networks are explored using two approaches: computer simulations of network
growth and a theoretical description based on a master equation. The results of
the two approaches are in excellent agreement. Special emphasis is put on the
investigation of the node degree probability distribution. It is found that the
tail of the distribution has the exponential form given by $exp(-k/m)$.
Implications of the node degree distribution with such tail characteristics are
briefly discussed. | cond-mat_dis-nn |
Finite temperature phase transition for disordered weakly interacting
bosons in one dimension: It is commonly accepted that there are no phase transitions in
one-dimensional (1D) systems at a finite temperature, because long-range
correlations are destroyed by thermal fluctuations. Here we demonstrate that
the 1D gas of short-range interacting bosons in the presence of disorder can
undergo a finite temperature phase transition between two distinct states:
fluid and insulator. None of these states has long-range spatial correlations,
but this is a true albeit non-conventional phase transition because transport
properties are singular at the transition point. In the fluid phase the mass
transport is possible, whereas in the insulator phase it is completely blocked
even at finite temperatures. We thus reveal how the interaction between
disordered bosons influences their Anderson localization. This key question,
first raised for electrons in solids, is now crucial for the studies of atomic
bosons where recent experiments have demonstrated Anderson localization in
expanding very dilute quasi-1D clouds. | cond-mat_dis-nn |
Z(2) Gauge Neural Network and its Phase Structure: We study general phase structures of neural-network models that have Z(2)
local gauge symmetry. The Z(2) spin variable Si = \pm1 on the i-th site
describes a neuron state as in the Hopfield model, and the Z(2) gauge variable
Jij = \pm1 describes a state of the synaptic connection between j-th and i-th
neurons. The gauge symmetry allows for a self-coupling energy among Jij's such
as JijJjkJki, which describes reverberation of signals. Explicitly, we consider
the three models; (I) annealed model with full and partial connections of Jij,
(II) quenched model with full connections where Jij is treated as a slow
quenched variable, and (III) quenched three-dimensional lattice model with the
nearest-neighbor connections. By numerical simulations, we examine their phase
structures paying attention to the effect of reverberation term, and compare
them each other and with the annealed 3D lattice model which has been studied
beforehand. By noting the dependence of thermodynamic quantities upon the total
number of sites and the connectivity among sites, we obtain a coherent
interpretation to understand these results. Among other things, we find that
the Higgs phase of the annealed model is separated into two stable spin-glass
phases in the quenched cases (II) and (III). | cond-mat_dis-nn |
Interacting particles at a metal-insulator transition: We study the influence of many-particle interaction in a system which, in the
single particle case, exhibits a metal-insulator transition induced by a finite
amount of onsite pontential fluctuations. Thereby, we consider the problem of
interacting particles in the one-dimensional quasiperiodic Aubry-Andre chain.
We employ the density-matrix renormalization scheme to investigate the finite
particle density situation. In the case of incommensurate densities, the
expected transition from the single-particle analysis is reproduced. Generally
speaking, interaction does not alter the incommensurate transition. For
commensurate densities, we map out the entire phase diagram and find that the
transition into a metallic state occurs for attractive interactions and
infinite small fluctuations -- in contrast to the case of incommensurate
densities. Our results for commensurate densities also show agreement with a
recent analytic renormalization group approach. | cond-mat_dis-nn |
Stability of the replica-symmetric solution in the
off-diagonally-disordered Bose-Hubbard model: We study a disordered system of interacting bosons described by the
Bose-Hubbard Hamiltonian with random tunneling amplitudes. We derive the
condition for the stability of the replica-symmetric solution for this model.
Following the scheme of de Almeida and Thouless, we determine if the solution
corresponds to the minimum of free energy by building the respective Hessian
matrix and checking its positive semidefiniteness. Thus, we find the
eigenvalues by postulating the set of eigenvectors based on their expected
symmetry, and require the eigenvalues to be non-negative. We evaluate the
spectrum numerically and identify matrix blocks that give rise to eigenvalues
that are always non-negative. Thus, we find a subset of eigenvalues coming from
decoupled subspaces that is sufficient to be checked as the stability
criterion. We also determine the stability of the phases present in the system,
finding that the disordered phase is stable, the glass phase is unstable, while
the superfluid phase has both stable and unstable parts. | cond-mat_dis-nn |
Phase transition for cutting-plane approach to vertex-cover problem: We study the vertex-cover problem which is an NP-hard optimization problem
and a prototypical model exhibiting phase transitions on random graphs, e.g.,
Erdoes-Renyi (ER) random graphs. These phase transitions coincide with changes
of the solution space structure, e.g, for the ER ensemble at connectivity
c=e=2.7183 from replica symmetric to replica-symmetry broken. For the
vertex-cover problem, also the typical complexity of exact branch-and-bound
algorithms, which proceed by exploring the landscape of feasible
configurations, change close to this phase transition from "easy" to "hard". In
this work, we consider an algorithm which has a completely different strategy:
The problem is mapped onto a linear programming problem augmented by a
cutting-plane approach, hence the algorithm operates in a space OUTSIDE the
space of feasible configurations until the final step, where a solution is
found. Here we show that this type of algorithm also exhibits an "easy-hard"
transition around c=e, which strongly indicates that the typical hardness of a
problem is fundamental to the problem and not due to a specific representation
of the problem. | cond-mat_dis-nn |
Intrinsic fluctuations in random lasers: We present a quantitative experimental and theoretical study of shot-to-shot
intensity fluctuations in the emitted light of a random laser. A model that
clarifies these intrinsic fluctuations is developed. We describe the output
versus input power graphs of the random laser with an effective spontaneous
emission factor (beta factor). | cond-mat_dis-nn |
Heat conduction and phonon localization in disordered harmonic crystals: We investigate the steady state heat current in two and three dimensional
isotopically disordered harmonic lattices. Using localization theory as well as
kinetic theory we estimate the system size dependence of the current. These
estimates are compared with numerical results obtained using an exact formula
for the current given in terms of a phonon transmission function, as well as by
direct nonequilibrium simulations. We find that heat conduction by
high-frequency modes is suppressed by localization while low-frequency modes
are strongly affected by boundary conditions. Our {\color{black}heuristic}
arguments show that Fourier's law is valid in a three dimensional disordered
solid except for special boundary conditions. We also study the pinned case
relevant to localization in quantum systems and often used as a model system to
study the validity of Fourier's law. Here we provide the first numerical
verification of Fourier's law in three dimensions. In the two dimensional
pinned case we find that localization of phonon modes leads to a heat
insulator. | cond-mat_dis-nn |
Physical realizability of small-world networks: Supplementing a lattice with long-range connections effectively models
small-world networks characterized by a high local and global
interconnectedness observed in systems ranging from society to the brain. If
the links have a wiring cost associated to their length l, the corresponding
distribution q(l) plays a crucial role. Uniform length distributions have
received most attention despite indications that q(l) ~ l^{-\alpha} exist, e.g.
for integrated circuits, the Internet and cortical networks. While length
distributions of this type were previously examined in the context of
navigability, we here discuss for such systems the emergence and physical
realizability of small-world topology. Our simple argument allows to understand
under which condition and at what expense a small world results. | cond-mat_dis-nn |
The effect of asymmetric disorder on the diffusion in arbitrary networks: Considering diffusion in the presence of asymmetric disorder, an exact
relationship between the strength of weak disorder and the electric resistance
of the corresponding resistor network is revealed, which is valid in arbitrary
networks. This implies that the dynamics are stable against weak asymmetric
disorder if the resistance exponent $\zeta$ of the network is negative. In the
case of $\zeta>0$, numerical analyses of the mean first-passage time $\tau$ on
various fractal lattices show that the logarithmic scaling of $\tau$ with the
distance $l$, $\ln\tau\sim l^{\psi}$, is a general rule, characterized by a new
dynamical exponent $\psi$ of the underlying lattice. | cond-mat_dis-nn |
Comment on "Critical point scaling of Ising spin glasses in a magnetic
field" by J. Yeo and M.A. Moore: In a section of a recent publication, [J. Yeo and M.A. Moore, Phys. Rev. B
91, 104432 (2015)], the authors discuss some of the arguments in the paper by
Parisi and Temesv\'ari [Nuclear Physics B 858, 293 (2012)]. In this comment, it
is shown how these arguments are misinterpreted, and the existence of the
Almeida-Thouless transition in the upper critical dimension 6 reasserted. | cond-mat_dis-nn |
Retrieval Phase Diagrams of Non-monotonic Hopfield Networks: We investigate the retrieval phase diagrams of an asynchronous
fully-connected attractor network with non-monotonic transfer function by means
of a mean-field approximation. We find for the noiseless zero-temperature case
that this non-monotonic Hopfield network can store more patterns than a network
with monotonic transfer function investigated by Amit et al. Properties of
retrieval phase diagrams of non-monotonic networks agree with the results
obtained by Nishimori and Opris who treated synchronous networks. We also
investigate the optimal storage capacity of the non-monotonic Hopfield model
with state-dependent synaptic couplings introduced by Zertuche et el. We show
that the non-monotonic Hopfield model with state-dependent synapses stores more
patterns than the conventional Hopfield model. Our formulation can be easily
extended to a general transfer function. | cond-mat_dis-nn |
Localization in 2D Quantum percolation: Quantum site percolation as a limiting case of binary alloy is studied
numerically in 2D within the tight-binding model. We address the transport
properties in all regimes - ballistic, diffusive (metallic), localized and
crossover between the latter two. Special attention is given to the region
close to the conduction band center, but even there the Anderson localization
persists, without signs of metal - insulator transition. We found standard
localization for sufficiently large samples. For smaller systems, novel partial
quantization of Landauer conductances, i. e. most values close to small
integers in arbitrary units is observed at band center. The crossover types of
conductance distributions (outside the band center) are found to be similar to
systems with corrugated surfaces. Universal conductance fluctuations in
metallic regime are shown to approach the known, theoretically predicted value.
The resonances in localized regime are Pendry necklaces. We tested Pendry's
conjecture on the probability of such rare conducting samples and it proved
consistent with our numerical results. | cond-mat_dis-nn |
Response to Comment on "Super-universality in Anderson localization"
arXiv:2210.10539v2: This is response to the recent comment arXiv:2210.10539v2 by I. Burmistrov. | cond-mat_dis-nn |
Hysteresis and Avalanches in the Random Anisotropy Ising Model: The behaviour of the Random Anisotropy Ising model at T=0 under local
relaxation dynamics is studied. The model includes a dominant ferromagnetic
interaction and assumes an infinite anisotropy at each site along local
anisotropy axes which are randomly aligned. Two different random distributions
of anisotropy axes have been studied. Both are characterized by a parameter
that allows control of the degree of disorder in the system. By using numerical
simulations we analyze the hysteresis loop properties and characterize the
statistical distribution of avalanches occuring during the metastable evolution
of the system driven by an external field. A disorder-induced critical point is
found in which the hysteresis loop changes from displaying a typical
ferromagnetic magnetization jump to a rather smooth loop exhibiting only tiny
avalanches. The critical point is characterized by a set of critical exponents,
which are consistent with the universal values proposed from the study of other
simpler models. | cond-mat_dis-nn |
Water adsorption on amorphous silica surfaces: A Car-Parrinello
simulation study: A combination of classical molecular dynamics (MD) and ab initio
Car-Parrinello molecular dynamics (CPMD) simulations is used to investigate the
adsorption of water on a free amorphous silica surface. From the classical MD
SiO_2 configurations with a free surface are generated which are then used as
starting configurations for the CPMD.We study the reaction of a water molecule
with a two-membered ring at the temperature T=300K. We show that the result of
this reaction is the formation of two silanol groups on the surface. The
activation energy of the reaction is estimated and it is shown that the
reaction is exothermic. | cond-mat_dis-nn |
The random Blume-Capel model on cubic lattice: first order inverse
freezing in a 3D spin-glass system: We present a numerical study of the Blume-Capel model with quenched disorder
in 3D. The phase diagram is characterized by spin-glass/paramagnet phase
transitions of both first and second order in the thermodynamic sense.
Numerical simulations are performed using the Exchange-Monte Carlo algorithm,
providing clear evidence for inverse freezing. The main features at criticality
and in the phase coexistence region are investigated. The whole inverse
freezing transition appears to be first order. The second order transition
appears to be in the same universality class of the Edwards-Anderson model. The
nature of the spin-glass phase is analyzed by means of the finite size scaling
behavior of the overlap distribution functions and the four-spins real-space
correlation functions. Evidence for a replica symmetry breaking-like
organization of states is provided. | cond-mat_dis-nn |
A ferromagnet with a glass transition: We introduce a finite-connectivity ferromagnetic model with a three-spin
interaction which has a crystalline (ferromagnetic) phase as well as a glass
phase. The model is not frustrated, it has a ferromagnetic equilibrium phase at
low temperature which is not reached dynamically in a quench from the
high-temperature phase. Instead it shows a glass transition which can be
studied in detail by a one step replica-symmetry broken calculation. This spin
model exhibits the main properties of the structural glass transition at a
solvable mean-field level. | cond-mat_dis-nn |
Transmission-eigenchannel velocity and diffusion: The diffusion model is used to calculate the time-averaged flow of particles
in stochastic media and the propagation of waves averaged over ensembles of
disordered static configurations. For classical waves exciting static
disordered samples, such as a layer of paint or a tissue sample, the flux
transmitted through the sample may be dramatically enhanced or suppressed
relative to predictions of diffusion theory when the sample is excited by a
waveform corresponding to a transmission eigenchannel. Even so, it is widely
acknowledged that the velocity of waves is irretrievably randomized in
scattering media. Here we demonstrate in microwave measurements and numerical
simulations that the statistics of velocity of different transmission
eigenchannels remain distinct on all length scales and are identical on the
incident and output surfaces. The interplay between eigenchannel velocities and
transmission eigenvalues determines the energy density within the medium, the
diffusion coefficient, and the dynamics of propagation. the diffusion
coefficient and all scatter9ng parameters, including the scattering mean free
path, oscillate with width of the sample as the number and shape of the
propagating channels in the medium change. | cond-mat_dis-nn |
Improved field theoretical approach to noninteracting Brownian particles
in a quenched random potential: We construct a dynamical field theory for noninteracting Brownian particles
in the presence of a quenched Gaussian random potential. The main variable for
the field theory is the density fluctuation which measures the difference
between the local density and its average value. The average density is
spatially inhomogeneous for given realization of the random potential. It
becomes uniform only after averaged over the disorder configurations. We
develop the diagrammatic perturbation theory for the density correlation
function and calculate the zero-frequency component of the response function
exactly by summing all the diagrams contributing to it. From this exact result
and the fluctuation dissipation relation, which holds in an equilibrium
dynamics, we find that the connected density correlation function always decays
to zero in the long-time limit for all values of disorder strength implying
that the system always remains ergodic. This nonperturbative calculation relies
on the simple diagrammatic structure of the present field theoretical scheme.
We compare in detail our diagrammatic perturbation theory with the one used in
a recent paper [B.\ Kim, M.\ Fuchs and V.\ Krakoviack, J.\ Stat.\ Mech.\ (2020)
023301], which uses the density fluctuation around the uniform average, and
discuss the difference in the diagrammatic structures of the two formulations. | cond-mat_dis-nn |
Sherrington-Kirkpatrick model near $T=T_c$: expanding around the Replica
Symmetric Solution: An expansion for the free energy functional of the Sherrington-Kirkpatrick
(SK) model, around the Replica Symmetric SK solution $Q^{({\rm RS})}_{ab} =
\delta_{ab} + q(1-\delta_{ab})$ is investigated. In particular, when the
expansion is truncated to fourth order in. $Q_{ab} - Q^{({\rm RS})}_{ab}$. The
Full Replica Symmetry Broken (FRSB) solution is explicitly found but it turns
out to exist only in the range of temperature $0.549...\leq T\leq T_c=1$, not
including T=0. On the other hand an expansion around the paramagnetic solution
$Q^{({\rm PM})}_{ab} = \delta_{ab}$ up to fourth order yields a FRSB solution
that exists in a limited temperature range $0.915...\leq T \leq T_c=1$. | cond-mat_dis-nn |
Percolation and jamming in random sequential adsorption of linear
segments on square lattice: We present the results of study of random sequential adsorption of linear
segments (needles) on sites of a square lattice. We show that the percolation
threshold is a nonmonotonic function of the length of the adsorbed needle,
showing a minimum for a certain length of the needles, while the jamming
threshold decreases to a constant with a power law. The ratio of the two
thresholds is also nonmonotonic and it remains constant only in a restricted
range of the needles length. We determine the values of the correlation length
exponent for percolation, jamming and their ratio. | cond-mat_dis-nn |
Strongly disordered spin ladders: The effect of quenched disorder on the low-energy properties of various
antiferromagnetic spin ladder models is studied by a numerical strong disorder
renormalization group method and by density matrix renormalization. For strong
enough disorder the originally gapped phases with finite topological or dimer
order become gapless. In these quantum Griffiths phases the scaling of the
energy, as well as the singularities in the dynamical quantities are
characterized by a finite dynamical exponent, z, which varies with the strength
of disorder. At the phase boundaries, separating topologically distinct
Griffiths phases the singular behavior of the disordered ladders is generally
controlled by an infinite randomness fixed point. | cond-mat_dis-nn |
Hierarchical neural networks perform both serial and parallel processing: In this work we study a Hebbian neural network, where neurons are arranged
according to a hierarchical architecture such that their couplings scale with
their reciprocal distance. As a full statistical mechanics solution is not yet
available, after a streamlined introduction to the state of the art via that
route, the problem is consistently approached through signal- to-noise
technique and extensive numerical simulations. Focusing on the low-storage
regime, where the amount of stored patterns grows at most logarithmical with
the system size, we prove that these non-mean-field Hopfield-like networks
display a richer phase diagram than their classical counterparts. In
particular, these networks are able to perform serial processing (i.e. retrieve
one pattern at a time through a complete rearrangement of the whole ensemble of
neurons) as well as parallel processing (i.e. retrieve several patterns
simultaneously, delegating the management of diff erent patterns to diverse
communities that build network). The tune between the two regimes is given by
the rate of the coupling decay and by the level of noise affecting the system.
The price to pay for those remarkable capabilities lies in a network's capacity
smaller than the mean field counterpart, thus yielding a new budget principle:
the wider the multitasking capabilities, the lower the network load and
viceversa. This may have important implications in our understanding of
biological complexity. | cond-mat_dis-nn |
Quantum-Mechanically Induced Asymmetry in the Phase Diagrams of
Spin-Glass Systems: The spin-1/2 quantum Heisenberg model is studied in all spatial dimensions d
by renormalization-group theory. Strongly asymmetric phase diagrams in
temperature and antiferromagnetic bond probability p are obtained in dimensions
d \geq 3. The asymmetry at high temperatures approaching the pure ferromagnetic
and antiferromagnetic systems disappears as d is increased. However, the
asymmetry at low but finite temperatures remains in all dimensions, with the
antiferromagnetic phase receding to the ferromagnetic phase. A
finite-temperature second-order phase boundary directly between the
ferromagnetic and antiferromagnetic phases occurs in d \geq 6, resulting in a
new multicritical point at its meeting with the boundaries to the paramagnetic
phase. In d=3,4,5, a paramagnetic phase reaching zero temperature intervenes
asymmetrically between the ferromagnetic and reentrant antiferromagnetic
phases. There is no spin-glass phase in any dimension. | cond-mat_dis-nn |
Real Space Renormalization Group Theory of Disordered Models of Glasses: We develop a real space renormalisation group analysis of disordered models
of glasses, in particular of the spin models at the origin of the Random First
Order Transition theory. We find three fixed points respectively associated to
the liquid state, to the critical behavior and to the glass state. The latter
two are zero-temperature ones; this provides a natural explanation of the
growth of effective activation energy scale and the concomitant huge increase
of relaxation time approaching the glass transition. The lower critical
dimension depends on the nature of the interacting degrees of freedom and is
higher than three for all models. This does not prevent three dimensional
systems from being glassy. Indeed, we find that their renormalisation group
flow is affected by the fixed points existing in higher dimension and in
consequence is non-trivial. Within our theoretical framework the glass
transition results to be an avoided phase transition. | cond-mat_dis-nn |
Thermal conductance of one dimensional disordered harmonic chains: We study heat conduction mediated by longitudinal phonons in one dimensional
disordered harmonic chains. Using scaling properties of the phonon density of
states and localization in disordered systems, we find non-trivial scaling of
the thermal conductance with the system size. Our findings are corroborated by
extensive numerical analysis. We show that a system with strong disorder,
characterized by a `heavy-tailed' probability distribution, and with large
impedance mismatch between the bath and the system satisfies Fourier's law. We
identify a dimensionless scaling parameter, related to the temperature scale
and the localization length of the phonons, through which the thermal
conductance for different models of disorder and different temperatures follows
a universal behavior. | cond-mat_dis-nn |
Quantitative analysis of a Schaffer collateral model: Advances in techniques for the formal analysis of neural networks have
introduced the possibility of detailed quantitative analyses of brain
circuitry. This paper applies a method for calculating mutual information to
the analysis of the Schaffer collateral connections between regions CA3 and CA1
of the hippocampus. Attention is given to the introduction of further details
of anatomy and physiology to the calculation: in particular, the distribution
of the number of connections that CA1 neurons receive from CA3, and the graded
nature of the firing-rate distribution in region CA3. | cond-mat_dis-nn |
Hexatic-Herringbone Coupling at the Hexatic Transition in Smectic Liquid
Crystals: 4-$ε$ Renormalization Group Calculations Revisited: Simple symmetry considerations would suggest that the transition from the
smectic-A phase to the long-range bond orientationally ordered hexatic
smectic-B phase should belong to the XY universality class. However, a number
of experimental studies have constantly reported over the past twenty years
"novel" critical behavior with non-XY critical exponents for this transition.
Bruinsma and Aeppli argued in Physical Review Letters {\bf 48}, 1625 (1982),
using a $4-\epsilon$ renormalization-group calculation, that short-range
molecular herringbone correlations coupled to the hexatic ordering drive this
transition first order via thermal fluctuations, and that the critical behavior
observed in real systems is controlled by a `nearby' tricritical point. We have
revisited the model of Bruinsma and Aeppli and present here the results of our
study. We have found two nontrivial strongly-coupled herringbone-hexatic fixed
points apparently missed by those authors. Yet, those two new nontrivial
fixed-points are unstable, and we obtain the same final conclusion as the one
reached by Bruinsma and Aeppli, namely that of a fluctuation-driven first order
transition. We also discuss the effect of local two-fold distortion of the bond
order as a possible missing order parameter in the Hamiltonian. | cond-mat_dis-nn |
Topological properties of hierarchical networks: Hierarchical networks are attracting a renewal interest for modelling the
organization of a number of biological systems and for tackling the complexity
of statistical mechanical models beyond mean-field limitations. Here we
consider the Dyson hierarchical construction for ferromagnets, neural networks
and spin-glasses, recently analyzed from a statistical-mechanics perspective,
and we focus on the topological properties of the underlying structures. In
particular, we find that such structures are weighted graphs that exhibit high
degree of clustering and of modularity, with small spectral gap; the robustness
of such features with respect to link removal is also studied. These outcomes
are then discussed and related to the statistical mechanics scenario in full
consistency. Lastly, we look at these weighted graphs as Markov chains and we
show that in the limit of infinite size, the emergence of ergodicity breakdown
for the stochastic process mirrors the emergence of meta-stabilities in the
corresponding statistical mechanical analysis. | cond-mat_dis-nn |
Statistics of anomalously localized states at the center of band E=0 in
the one-dimensional Anderson localization model: We consider the distribution function $P(|\psi|^{2})$ of the eigenfunction
amplitude at the center-of-band (E=0) anomaly in the one-dimensional
tight-binding chain with weak uncorrelated on-site disorder (the
one-dimensional Anderson model). The special emphasis is on the probability of
the anomalously localized states (ALS) with $|\psi|^{2}$ much larger than the
inverse typical localization length $\ell_{0}$. Using the solution to the
generating function $\Phi_{an}(u,\phi)$ found recently in our works we find the
ALS probability distribution $P(|\psi|^{2})$ at $|\psi|^{2}\ell_{0} >> 1$. As
an auxiliary preliminary step we found the asymptotic form of the generating
function $\Phi_{an}(u,\phi)$ at $u >> 1$ which can be used to compute other
statistical properties at the center-of-band anomaly. We show that at
moderately large values of $|\psi|^{2}\ell_{0}$, the probability of ALS at E=0
is smaller than at energies away from the anomaly. However, at very large
values of $|\psi|^{2}\ell_{0}$, the tendency is inverted: it is exponentially
easier to create a very strongly localized state at E=0 than at energies away
from the anomaly. We also found the leading term in the behavior of
$P(|\psi|^{2})$ at small $|\psi|^{2}<< \ell_{0}^{-1}$ and show that it is
consistent with the exponential localization corresponding to the Lyapunov
exponent found earlier by Kappus and Wegner and Derrida and Gardner. | cond-mat_dis-nn |
Anderson localization of one-dimensional hybrid particles: We solve the Anderson localization problem on a two-leg ladder by the
Fokker-Planck equation approach. The solution is exact in the weak disorder
limit at a fixed inter-chain coupling. The study is motivated by progress in
investigating the hybrid particles such as cavity polaritons. This application
corresponds to parametrically different intra-chain hopping integrals (a "fast"
chain coupled to a "slow" chain). We show that the canonical
Dorokhov-Mello-Pereyra-Kumar (DMPK) equation is insufficient for this problem.
Indeed, the angular variables describing the eigenvectors of the transmission
matrix enter into an extended DMPK equation in a non-trivial way, being
entangled with the two transmission eigenvalues. This extended DMPK equation is
solved analytically and the two Lyapunov exponents are obtained as functions of
the parameters of the disordered ladder. The main result of the paper is that
near the resonance energy, where the dispersion curves of the two decoupled and
disorder-free chains intersect, the localization properties of the ladder are
dominated by those of the slow chain. Away from the resonance they are
dominated by the fast chain: a local excitation on the slow chain may travel a
distance of the order of the localization length of the fast chain. | cond-mat_dis-nn |
Routes towards Anderson-Like localization of Bose-Einstein condensates
in disordered optical lattices: We investigate, both experimentally and theoretically, possible routes
towards Anderson-like localization of Bose-Einstein condensates in disordered
potentials. The dependence of this quantum interference effect on the nonlinear
interactions and the shape of the disorder potential is investigated.
Experiments with an optical lattice and a superimposed disordered potential
reveal the lack of Anderson localization. A theoretical analysis shows that
this absence is due to the large length scale of the disorder potential as well
as its screening by the nonlinear interactions. Further analysis shows that
incommensurable superlattices should allow for the observation of the
cross-over from the nonlinear screening regime to the Anderson localized case
within realistic experimental parameters. | cond-mat_dis-nn |
Slow Dynamics in a Two-Dimensional Anderson-Hubbard Model: We study the real-time dynamics of a two-dimensional Anderson--Hubbard model
using nonequilibrium self-consistent perturbation theory within the second-Born
approximation. When compared with exact diagonalization performed on small
clusters, we demonstrate that for strong disorder this technique approaches the
exact result on all available timescales, while for intermediate disorder, in
the vicinity of the many-body localization transition, it produces
quantitatively accurate results up to nontrivial times. Our method allows for
the treatment of system sizes inaccessible by any numerically exact method and
for the complete elimination of finite size effects for the times considered.
We show that for a sufficiently strong disorder the system becomes nonergodic,
while for intermediate disorder strengths and for all accessible time scales
transport in the system is strictly subdiffusive. We argue that these results
are incompatible with a simple percolation picture, but are consistent with the
heuristic random resistor network model where subdiffusion may be observed for
long times until a crossover to diffusion occurs. The prediction of slow
finite-time dynamics in a two-dimensional interacting and disordered system can
be directly verified in future cold atoms experiments | cond-mat_dis-nn |
Ideal quantum glass transitions: many-body localization without quenched
disorder: We explore the possibility for translationally invariant quantum many-body
systems to undergo a dynamical glass transition, at which ergodicity and
translational invariance break down spontaneously, driven entirely by quantum
effects. In contrast to analogous classical systems, where the existence of
such an ideal glass transition remains a controversial issue, a genuine phase
transition is predicted in the quantum regime. This ideal quantum glass
transition can be regarded as a many-body localization transition due to
self-generated disorder. Despite their lack of thermalization, these
disorder-free quantum glasses do not possess an extensive set of local
conserved operators, unlike what is conjectured for many-body localized systems
with strong quenched disorder. | cond-mat_dis-nn |
Origin of the Growing Length Scale in M-p-Spin Glass Models: Two versions of the M-p-spin glass model have been studied with the
Migdal-Kadanoff renormalization group approximation. The model with p=3 and M=3
has at mean-field level the ideal glass transition at the Kauzmann temperature
and at lower temperatures still the Gardner transition to a state like that of
an Ising spin glass in a field. The model with p=3 and M=2 has only the Gardner
transition. In the dimensions studied, d=2,3 and 4, both models behave almost
identically, indicating that the growing correlation length as the temperature
is reduced in these models -- the analogue of the point-to-set length scale --
is not due to the mechanism postulated in the random first order transition
theory of glasses, but is more like that expected on the analogy of glasses to
the Ising spin glass in a field. | cond-mat_dis-nn |
Absence of the diffusion pole in the Anderson insulator: We discuss conditions for the existence of the diffusion pole and its
consequences in disordered noninteracting electron systems. Using only
nonperturbative and exact arguments we find against expectations that the
diffusion pole can exist only in the diffusive (metallic) regime. We
demonstrate that the diffusion pole in the Anderson localization phase would
lead to nonexistence of the self-energy and hence to a physically inconsistent
picture. The way how to consistently treat and understand the Anderson
localization transition with vanishing of the diffusion pole is presented. | cond-mat_dis-nn |
Scaling Law and Aging Phenomena in the Random Energy Model: We study the effect of temperature shift on aging phenomena in the Random
Energy Model (REM). From calculation on the correlation function and simulation
on the Zero-Field-Cooled magnetization, we find that the REM satisfies a
scaling relation even if temperature is shifted. Furthermore, this scaling
property naturally leads to results obtained in experiment and the droplet
theory. | cond-mat_dis-nn |
Many-body localization of ${\mathbb Z}_3$ Fock parafermions: We study the effects of a random magnetic field on a one-dimensional (1D)
spin-1 chain with {\it correlated} nearest-neighbor $XY$ interaction. We show
that this spin model can be exactly mapped onto the 1D disordered tight-binding
model of ${\mathbb Z}_3$ Fock parafermions (FPFs), exotic anyonic
quasiparticles that generalize usual spinless fermions. Thus, we have a
peculiar case of a disordered Hamiltonian that, despite being bilinear in the
creation and annihilation operators, exhibits a many-body localization (MBL)
transition owing to the nontrivial statistics of FPFs. This is in sharp
contrast to conventional bosonic and fermionic quadratic disordered
Hamiltonians that show single-particle (Anderson) localization. We perform
finite-size exact diagonalization calculations of level-spacing statistics,
fractal dimensions, and entanglement entropy, and provide convincing evidence
for the MBL transition at finite disorder strength. | cond-mat_dis-nn |
Topological phases of amorphous matter: Topological phases of matter are often understood and predicted with the help
of crystal symmetries, although they don't rely on them to exist. In this
chapter we review how topological phases have been recently shown to emerge in
amorphous systems. We summarize the properties of topological states and
discuss how disposing of translational invariance has motivated the surge of
new tools to characterize topological states in amorphous systems, both
theoretically and experimentally. The ubiquity of amorphous systems combined
with the robustness of topology has the potential to bring new fundamental
understanding in our classification of phases of matter, and inspire new
technological developments. | cond-mat_dis-nn |
Conductance distribution in 1D systems: dependence on the Fermi level
and the ideal leads: The correct definition of the conductance of finite systems implies a
connection to the system of the massive ideal leads. Influence of the latter on
the properties of the system appears to be rather essential and is studied
below on the simplest example of the 1D case. In the log-normal regime this
influence is reduced to the change of the absolute scale of conductance, but
generally changes the whole distribution function. Under the change of the
system length L, its resistance may undergo the periodic or aperiodic
oscillations. Variation of the Fermi level induces qualitative changes in the
conductance distribution, resembling the smoothed Anderson transition. | cond-mat_dis-nn |
Spin glass behavior in a random Coulomb antiferromagnet: We study spin glass behavior in a random Ising Coulomb antiferromagnet in two
and three dimensions using Monte Carlo simulations. In two dimensions, we find
a transition at zero temperature with critical exponents consistent with those
of the Edwards Anderson model, though with large uncertainties. In three
dimensions, evidence for a finite-temperature transition, as occurs in the
Edwards-Anderson model, is rather weak. This may indicate that the sizes are
too small to probe the asymptotic critical behavior, or possibly that the
universality class is different from that of the Edwards-Anderson model and has
a lower critical dimension equal to three. | cond-mat_dis-nn |
Laplacian Coarse Graining in Complex Networks: Complex networks can model a range of different systems, from the human brain
to social connections. Some of those networks have a large number of nodes and
links, making it impractical to analyze them directly. One strategy to simplify
these systems is by creating miniaturized versions of the networks that keep
their main properties. A convenient tool that applies that strategy is the
renormalization group (RG), a methodology used in statistical physics to change
the scales of physical systems. This method consists of two steps: a coarse
grain, where one reduces the size of the system, and a rescaling of the
interactions to compensate for the information loss. This work applies RG to
complex networks by introducing a coarse-graining method based on the Laplacian
matrix. We use a field-theoretical approach to calculate the correlation
function and coarse-grain the most correlated nodes into super-nodes, applying
our method to several artificial and real-world networks. The results are
promising, with most of the networks under analysis showing self-similar
properties across different scales. | cond-mat_dis-nn |
Spatial correlations in the relaxation of the Kob-Andersen model: We describe spatio-temporal correlations and heterogeneities in a kinetically
constrained glassy model, the Kob-Andersen model. The kinetic constraints of
the model alone induce the existence of dynamic correlation lengths, that
increase as the density $\rho$ increases, in a way compatible with a
double-exponential law. We characterize in detail the trapping time correlation
length, the cooperativity length, and the distribution of persistent clusters
of particles. This last quantity is related to the typical size of blocked
clusters that slow down the dynamics for a given density. | cond-mat_dis-nn |
TASEP Exit Times: We address the question of the time needed by $N$ particles, initially
located on the first sites of a finite 1D lattice of size $L$, to exit that
lattice when they move according to a TASEP transport model. Using analytical
calculations and numerical simulations, we show that when $N \ll L$, the mean
exit time of the particles is asymptotically given by $T_N(L) \sim L+\beta_N
\sqrt{L}$ for large lattices. Building upon exact results obtained for 2
particles, we devise an approximate continuous space and time description of
the random motion of the particles that provides an analytical recursive
relation for the coefficients $\beta_N$. The results are shown to be in very
good agreement with numerical results. This approach sheds some light on the
exit dynamics of $N$ particles in the regime where $N$ is finite while the
lattice size $L\rightarrow \infty$. This complements previous asymptotic
results obtained by Johansson in \cite{Johansson2000} in the limit where both
$N$ and $L$ tend to infinity while keeping the particle density $N/L$ finite. | cond-mat_dis-nn |
Out of equilibrium Phase Diagram of the Quantum Random Energy Model: In this paper we study the out-of-equilibrium phase diagram of the quantum
version of Derrida's Random Energy Model, which is the simplest model of
mean-field spin glasses. We interpret its corresponding quantum dynamics in
Fock space as a one-particle problem in very high dimension to which we apply
different theoretical methods tailored for high-dimensional lattices: the
Forward-Scattering Approximation, a mapping to the Rosenzweig-Porter model, and
the cavity method. Our results indicate the existence of two transition lines
and three distinct dynamical phases: a completely many-body localized phase at
low energy, a fully ergodic phase at high energy, and a multifractal "bad
metal" phase at intermediate energy. In the latter, eigenfunctions occupy a
diverging volume, yet an exponentially vanishing fraction of the total Hilbert
space. We discuss the limitations of our approximations and the relationship
with previous studies. | cond-mat_dis-nn |
Hysteresis, Avalanches, and Noise: Numerical Methods: In studying the avalanches and noise in a model of hysteresis loops we have
developed two relatively straightforward algorithms which have allowed us to
study large systems efficiently. Our model is the random-field Ising model at
zero temperature, with deterministic albeit random dynamics. The first
algorithm, implemented using sorted lists, scales in computer time as O(N log
N), and asymptotically uses N (sizeof(double)+ sizeof(int)) bits of memory. The
second algorithm, which never generates the random fields, scales in time as
O(N \log N) and asymptotically needs storage of only one bit per spin, about 96
times less memory than the first algorithm. We present results for system sizes
of up to a billion spins, which can be run on a workstation with 128MB of RAM
in a few hours. We also show that important physical questions were resolved
only with the largest of these simulations. | cond-mat_dis-nn |
Antagonistic interactions can stabilise fixed points in heterogeneous
linear dynamical systems: We analyse the stability of large, linear dynamical systems of variables that
interact through a fully connected random matrix and have inhomogeneous growth
rates. We show that in the absence of correlations between the coupling
strengths, a system with interactions is always less stable than a system
without interactions. Contrarily to the uncorrelated case, interactions that
are antagonistic, i.e., characterised by negative correlations, can stabilise
linear dynamical systems. In particular, when the strength of the interactions
is not too strong, systems with antagonistic interactions are more stable than
systems without interactions. These results are obtained with an exact theory
for the spectral properties of fully connected random matrices with diagonal
disorder. | cond-mat_dis-nn |
Navigating Networks with Limited Information: We study navigation with limited information in networks and demonstrate that
many real-world networks have a structure which can be described as favoring
communication at short distance at the cost of constraining communication at
long distance. This feature, which is robust and more evident with limited than
with complete information, reflects both topological and possibly functional
design characteristics. For example, the characteristics of the networks
studied derived from a city and from the Internet are manifested through
modular network designs. We also observe that directed navigation in typical
networks requires remarkably little information on the level of individual
nodes. By studying navigation, or specific signaling, we take a complementary
approach to the common studies of information transfer devoted to broadcasting
of information in studies of virus spreading and the like. | cond-mat_dis-nn |
Systematic Series Expansions for Processes on Networks: We use series expansions to study dynamics of equilibrium and non-equilibrium
systems on networks. This analytical method enables us to include detailed
non-universal effects of the network structure. We show that even low order
calculations produce results which compare accurately to numerical simulation,
while the results can be systematically improved. We show that certain commonly
accepted analytical results for the critical point on networks with a broad
degree distribution need to be modified in certain cases due to
disassortativity; the present method is able to take into account the
assortativity at sufficiently high order, while previous results correspond to
leading and second order approximations in this method. Finally, we apply this
method to real-world data. | cond-mat_dis-nn |
Interface fluctuations in disordered systems: Universality and
non-Gaussian statistics: We employ a functional renormalization group to study interfaces in the
presence of a pinning potential in $d=4-\epsilon$ dimensions. In contrast to a
previous approach [D.S. Fisher, Phys. Rev. Lett. {\bf 56}, 1964 (1986)] we use
a soft-cutoff scheme. With the method developed here we confirm the value of
the roughness exponent $\zeta \approx 0.2083 \epsilon$ in order $\epsilon$.
Going beyond previous work, we demonstrate that this exponent is universal. In
addition, we analyze the generation of higher cumulants in the disorder
distribution and the role of temperature as a dangerously irrelevant variable. | cond-mat_dis-nn |
Dynamic Gardner crossover in a simple structural glass: The criticality of the jamming transition responsible for amorphous
solidification has been theoretically linked to the marginal stability of a
thermodynamic Gardner phase. While the critical exponents of jamming appear
independent of the preparation history, the pertinence of Gardner physics far
from equilibrium is an open question. To fill this gap, we numerically study
the nonequilibrium dynamics of hard disks compressed towards the jamming
transition using a broad variety of protocols. We show that dynamic signatures
of Gardner physics can be disentangled from the aging relaxation dynamics. We
thus define a generic dynamic Gardner crossover regardless of the history. Our
results show that the jamming transition is always accessed by exploring
increasingly complex landscape, resulting in the anomalous microscopic
relaxation dynamics that remains to be understood theoretically. | cond-mat_dis-nn |
Optical response of electrons in a random potential: Using our recently developed Chebyshev expansion technique for
finite-temperature dynamical correlation functions we numerically study the AC
conductivity $\sigma(\omega)$ of the Anderson model on large cubic clusters of
up to $100^3$ sites. Extending previous results we focus on the role of the
boundary conditions and check the consistency of the DC limit, $\omega\to 0$,
by comparing with direct conductance calculations based on a Greens function
approach in a Landauer B\"uttiker type setup. | cond-mat_dis-nn |
Free energy landscapes, dynamics and the edge of chaos in mean-field
models of spin glasses: Metastable states in Ising spin-glass models are studied by finding iterative
solutions of mean-field equations for the local magnetizations. Two different
equations are studied: the TAP equations which are exact for the SK model, and
the simpler `naive-mean-field' (NMF) equations. The free-energy landscapes that
emerge are very different. For the TAP equations, the numerical studies confirm
the analytical results of Aspelmeier et al., which predict that TAP states
consist of close pairs of minima and index-one (one unstable direction) saddle
points, while for the NMF equations saddle points with large indices are found.
For TAP the barrier height between a minimum and its nearby saddle point scales
as (f-f_0)^{-1/3} where f is the free energy per spin of the solution and f_0
is the equilibrium free energy per spin. This means that for `pure states', for
which f-f_0 is of order 1/N, the barriers scale as N^{1/3}, but between states
for which f-f_0 is of order one the barriers are finite and also small so such
metastable states will be of limited physical significance. For the NMF
equations there are saddles of index K and we can demonstrate that their
complexity Sigma_K scales as a function of K/N. We have also employed an
iterative scheme with a free parameter that can be adjusted to bring the system
of equations close to the `edge of chaos'. Both for the TAP and NME equations
it is possible with this approach to find metastable states whose free energy
per spin is close to f_0. As N increases, it becomes harder and harder to find
solutions near the edge of chaos, but nevertheless the results which can be
obtained are competitive with those achieved by more time-consuming computing
methods and suggest that this method may be of general utility. | cond-mat_dis-nn |
Modular synchronization in complex networks with a gauge Kuramoto model: We modify the Kuramoto model for synchronization on complex networks by
introducing a gauge term that depends on the edge betweenness centrality (BC).
The gauge term introduces additional phase difference between two vertices from
0 to $\pi$ as the BC on the edge between them increases from the minimum to the
maximum in the network. When the network has a modular structure, the model
generates the phase synchronization within each module, however, not over the
entire system. Based on this feature, we can distinguish modules in complex
networks, with relatively little computational time of $\mathcal{O}(NL)$, where
$N$ and $L$ are the number of vertices and edges in the system, respectively.
We also examine the synchronization of the modified Kuramoto model and compare
it with that of the original Kuramoto model in several complex networks. | cond-mat_dis-nn |
Statistics of Resonances and Delay Times in Random Media: Beyond Random
Matrix Theory: We review recent developments on quantum scattering from mesoscopic systems.
Various spatial geometries whose closed analogs shows diffusive, localized or
critical behavior are considered. These are features that cannot be described
by the universal Random Matrix Theory results. Instead one has to go beyond
this approximation and incorporate them in a non-perturbative way. Here, we pay
particular emphasis to the traces of these non-universal characteristics, in
the distribution of the Wigner delay times and resonance widths. The former
quantity captures time dependent aspects of quantum scattering while the latter
is associated with the poles of the scattering matrix. | cond-mat_dis-nn |
Interplay and competition between disorder and flat band in an
interacting Creutz ladder: We clarify the interplay and competition between disorder and flat band in
the Creutz ladder with inter-particle interactions focusing on the system's
dynamics. Without disorder, the Creutz ladder exhibits flat-band many-body
localization (FMBL). In this work, we find that disorder generates drastic
effects on the system, i.e., addition of it induces a thermal phase first and
further increase of it leads the system to the conventional many-body-localized
(MBL) phase. The competition gives novel localization properties and
unconventional quench dynamics to the system. We first draw the global sketch
of the localization phase diagram by focusing on the two-particle system. The
thermal phase intrudes between the FMBL and MBL phases, the regime of which
depends on the strength of disorder and interactions. Based on the two-particle
phase diagram and the properties of the quench dynamics, we further investigate
finite-filling cases in detail. At finite-filling fractions, we again find that
the interplay/competition between the interactions and disorder in the original
flat-band Creutz ladder induces thermal phase, which separates the FMBL and MBL
phases. We also verify that the time evolution of the system coincides with the
static phase diagrams. For suitable fillings, the conservation of the
initial-state information and low-growth entanglement dynamics are also
observed. These properties depend on the strength of disorder and interactions. | cond-mat_dis-nn |
Instantons in the working memory: implications for schizophrenia: The influence of the synaptic channel properties on the stability of delayed
activity maintained by recurrent neural network is studied. The duration of
excitatory post-synaptic current (EPSC) is shown to be essential for the global
stability of the delayed response. NMDA receptor channel is a much more
reliable mediator of the reverberating activity than AMPA receptor, due to a
longer EPSC. This allows to interpret the deterioration of working memory
observed in the NMDA channel blockade experiments. The key mechanism leading to
the decay of the delayed activity originates in the unreliability of the
synaptic transmission. The optimum fluctuation of the synaptic conductances
leading to the decay is identified. The decay time is calculated analytically
and the result is confirmed computationally. | cond-mat_dis-nn |
Criticality and entanglement in random quantum systems: We review studies of entanglement entropy in systems with quenched
randomness, concentrating on universal behavior at strongly random quantum
critical points. The disorder-averaged entanglement entropy provides insight
into the quantum criticality of these systems and an understanding of their
relationship to non-random ("pure") quantum criticality. The entanglement near
many such critical points in one dimension shows a logarithmic divergence in
subsystem size, similar to that in the pure case but with a different universal
coefficient. Such universal coefficients are examples of universal critical
amplitudes in a random system. Possible measurements are reviewed along with
the one-particle entanglement scaling at certain Anderson localization
transitions. We also comment briefly on higher dimensions and challenges for
the future. | cond-mat_dis-nn |
Gauged Neural Network: Phase Structure, Learning, and Associative Memory: A gauge model of neural network is introduced, which resembles the Z(2) Higgs
lattice gauge theory of high-energy physics. It contains a neuron variable $S_x
= \pm 1$ on each site $x$ of a 3D lattice and a synaptic-connection variable
$J_{x\mu} = \pm 1$ on each link $(x,x+\hat{\mu}) (\mu=1,2,3)$. The model is
regarded as a generalization of the Hopfield model of associative memory to a
model of learning by converting the synaptic weight between $x$ and
$x+\hat{\mu}$ to a dynamical Z(2) gauge variable $J_{x\mu}$. The local Z(2)
gauge symmetry is inherited from the Hopfield model and assures us the locality
of time evolutions of $S_x$ and $J_{x\mu}$ and a generalized Hebbian learning
rule. At finite "temperatures", numerical simulations show that the model
exhibits the Higgs, confinement, and Coulomb phases. We simulate dynamical
processes of learning a pattern of $S_x$ and recalling it, and classify the
parameter space according to the performance. At some parameter regions, stable
column-layer structures in signal propagations are spontaneously generated.
Mutual interactions between $S_x$ and $J_{x\mu}$ induce partial memory loss as
expected. | cond-mat_dis-nn |
Super-Rough Glassy Phase of the Random Field XY Model in Two Dimensions: We study both analytically, using the renormalization group (RG) to two loop
order, and numerically, using an exact polynomial algorithm, the
disorder-induced glass phase of the two-dimensional XY model with quenched
random symmetry-breaking fields and without vortices. In the super-rough glassy
phase, i.e. below the critical temperature $T_c$, the disorder and thermally
averaged correlation function $B(r)$ of the phase field $\theta(x)$, $B(r) =
\bar{<[\theta(x) - \theta(x+ r) ]^2>}$ behaves, for $r \gg a$, as $B(r) \simeq
A(\tau) \ln^2 (r/a)$ where $r = |r|$ and $a$ is a microscopic length scale. We
derive the RG equations up to cubic order in $\tau = (T_c-T)/T_c$ and predict
the universal amplitude ${A}(\tau) = 2\tau^2-2\tau^3 + {\cal O}(\tau^4)$. The
universality of $A(\tau)$ results from nontrivial cancellations between
nonuniversal constants of RG equations. Using an exact polynomial algorithm on
an equivalent dimer version of the model we compute ${A}(\tau)$ numerically and
obtain a remarkable agreement with our analytical prediction, up to $\tau
\approx 0.5$. | cond-mat_dis-nn |
Low Temperature Properties of the Random Field Potts Chain: The random field q-States Potts model is investigated using exact
groundstates and finite-temperature transfer matrix calculations. It is found
that the domain structure and the Zeeman energy of the domains resembles for
general q the random field Ising case (q=2), which is also the expectation
based on a random-walk picture of the groundstate. The domain size distribution
is exponential, and the scaling of the average domain size with the disorder
strength is similar for q arbitrary. The zero-temperature properties are
compared to the equilibrium spin states at small temperatures, to investigate
the effect of local random field fluctuations that imply locally degenerate
regions. The response to field pertubabtions ('chaos') and the susceptibility
are investigated. In particular for the chaos exponent it is found to be 1 for
q = 2,...,5. Finally for q=2 (Ising case) the domain length distribution is
studied for correlated random fields. | cond-mat_dis-nn |
Deformation of inherent structures to detect long-range correlations in
supercooled liquids: We propose deformations of inherent structures as a suitable tool for
detecting structural changes underlying the onset of cooperativity in
supercooled liquids. The non-affine displacement (NAD) field resulting from the
applied deformation shows characteristic differences between the high
temperature liquid and supercooled state, that are typically observed in
dynamic quantities. The average magnitude of the NAD is very sensitive to
temperature changes in the supercooled regime and is found to be strongly
correlated with the inherent structure energy. In addition, the NAD field is
characterized by a correlation length that increases upon lowering the
temperature towards the supercooled regime. | cond-mat_dis-nn |
Holes in a Quantum Spin Liquid: Magnetic neutron scattering provides evidence for nucleation of
antiferromagnetic droplets around impurities in a doped nickel-oxide based
quantum magnet. The undoped parent compound contains a spin liquid with a
cooperative singlet ground state and a gap in the magnetic excitation spectrum.
Calcium doping creates excitations below the gap with an incommensurate
structure factor. We show that weakly interacting antiferromagnetic droplets
with a central phase shift of $\pi$ and a size controlled by the correlation
length of the quantum liquid can account for the data. The experiment provides
a first quantitative impression of the magnetic polarization cloud associated
with holes in a doped transition metal oxide. | cond-mat_dis-nn |
Soft annealing: A new approach to difficult computational problems: I propose a new method to study computationally difficult problems. I
consider a new system, larger than the one I want to simulate. The original
system is recovered by imposing constraints on the large system. I simulate the
large system with the hard constraints replaced by soft constraints. I
illustrate the method in the case of the ferromagnetic Ising model and in the
case the three dimensional spin-glass model. I show that in both models the
phases of the soft problem have the same properties as the phases of the
original model and that the softened model belongs to the same universality
class as the original one. I show that correlation times are much shorter in
the larger soft constrained system and that it is computationally advantageous
to study it instead of the original system. This method is quite general and
can be applied to many other systems. | cond-mat_dis-nn |
Dynamical Gauge Theory for the XY Gauge Glass Model: Dynamical systems of the gauge glass are investigated by the method of the
gauge transformation.Both stochastic and deterministic dynamics are treated.
Several exact relations are derived among dynamical quantities such as
equilibrium and nonequilibrium auto-correlation functions, relaxation functions
of order parameter and internal energy. They provide physical properties in
terms of dynamics in the SG phase, a possible mixed phase and the Griffiths
phase, the multicritical dynamics and the aging phenomenon. We also have a
plausible argument for the absence of re-entrant transition in two or higher
dimensions. | cond-mat_dis-nn |
On the number of limit cycles in asymmetric neural networks: The comprehension of the mechanisms at the basis of the functioning of
complexly interconnected networks represents one of the main goals of
neuroscience. In this work, we investigate how the structure of recurrent
connectivity influences the ability of a network to have storable patterns and
in particular limit cycles, by modeling a recurrent neural network with
McCulloch-Pitts neurons as a content-addressable memory system.
A key role in such models is played by the connectivity matrix, which, for
neural networks, corresponds to a schematic representation of the "connectome":
the set of chemical synapses and electrical junctions among neurons. The shape
of the recurrent connectivity matrix plays a crucial role in the process of
storing memories. This relation has already been exposed by the work of Tanaka
and Edwards, which presents a theoretical approach to evaluate the mean number
of fixed points in a fully connected model at thermodynamic limit.
Interestingly, further studies on the same kind of model but with a finite
number of nodes have shown how the symmetry parameter influences the types of
attractors featured in the system. Our study extends the work of Tanaka and
Edwards by providing a theoretical evaluation of the mean number of attractors
of any given length $L$ for different degrees of symmetry in the connectivity
matrices. | cond-mat_dis-nn |
Vogel-Fulcher freezing in relaxor ferroelectrics: A physical mechanism for the freezing of polar nanoregions (PNRs) in relaxor
ferroelectrics is presented. Assuming that the activation energy for the
reorientation of a cluster of PNRs scales with the mean volume of the cluster,
the characteristic relaxation time $\tau$ is found to diverge as the cluster
volume reaches the percolation limit. Applying the mean field theory of
continuum percolation, the familiar Vogel-Fulcher equation for the temperature
dependence of $\tau$ is derived. | cond-mat_dis-nn |
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