text
stringlengths 89
2.49k
| category
stringclasses 19
values |
|---|---|
Temperature-dependent criticality in random 2D Ising models: We consider 2D random Ising ferromagnetic models, where quenched disorder is
represented either by random local magnetic fields (Random Field Ising Model)
or by a random distribution of interaction couplings (Random Bond Ising Model).
In both cases we first perform zero- and finite-temperature Monte-Carlo
simulations to determine how the critical temperature depends on the disorder
parameter. We then focus on the reversal transition triggered by an external
field, and study the associated Barkhausen noise. Our main result is that the
critical exponents characterizing the power-law associated with the Barkhausen
noise exhibit a temperature dependence in line with existing experimental
observations. | cond-mat_dis-nn |
Dynamics of weakly coupled random antiferromagnetic quantum spin chains: We study the low-energy collective excitations and dynamical response
functions of weakly coupled random antiferromagnetic spin-1/2 chains. The
interchain coupling leads to Neel order at low temperatures. We use the
real-space renormalization group technique to tackle the intrachain couplings
and treat the interchain couplings within the Random Phase Approximation (RPA).
We show that the system supports collective spin wave excitations, and
calculate the spin wave velocity and spectra weight within RPA. Comparisons
will be made with inelastic neutron scattering experiments
quasi-one-dimensional disordered spin systems such as doped CuGeO$_3$ | cond-mat_dis-nn |
The Exponential Capacity of Dense Associative Memories: Recent generalizations of the Hopfield model of associative memories are able
to store a number $P$ of random patterns that grows exponentially with the
number $N$ of neurons, $P=\exp(\alpha N)$. Besides the huge storage capacity,
another interesting feature of these networks is their connection to the
attention mechanism which is part of the Transformer architectures widely
applied in deep learning. In this work, we study a generic family of pattern
ensembles using a statistical mechanics analysis which gives exact asymptotic
thresholds for the retrieval of a typical pattern, $\alpha_1$, and lower bounds
for the maximum of the load $\alpha$ for which all patterns can be retrieved,
$\alpha_c$, as well as sizes of attraction basins. We discuss in detail the
cases of Gaussian and spherical patterns, and show that they display rich and
qualitatively different phase diagrams. | cond-mat_dis-nn |
Renormalization of Oscillator Lattices with Disorder: A real-space renormalization transformation is constructed for lattices of
non-identical oscillators with dynamics of the general form
$d\phi_{k}/dt=\omega_{k}+g\sum_{l}f_{lk}(\phi_{l},\phi_{k})$. The
transformation acts on ensembles of such lattices. Critical properties
corresponding to a second order phase transition towards macroscopic
synchronization are deduced. The analysis is potentially exact, but relies in
part on unproven assumptions. Numerically, second order phase transitions with
the predicted properties are observed as $g$ increases in two structurally
different, two-dimensional oscillator models. One model has smooth coupling
$f_{lk}(\phi_{l},\phi_{k})=\phi(\phi_{l}-\phi_{k})$, where $\phi(x)$ is
non-odd. The other model is pulse-coupled, with
$f_{lk}(\phi_{l},\phi_{k})=\delta(\phi_{l})\phi(\phi_{k})$. Lower bounds for
the critical dimensions for different types of coupling are obtained. For
non-odd coupling, macroscopic synchronization cannot be ruled out for any
dimension $D\geq 1$, whereas in the case of odd coupling, the well-known result
that it can be ruled out for $D< 3$ is regained. | cond-mat_dis-nn |
Numerical verification of universality for the Anderson transition: We analyze the scaling behavior of the higher Lyapunov exponents at the
Anderson transition. We estimate the critical exponent and verify its
universality and that of the critical conductance distribution for box,
Gaussian and Lorentzian distributions of the random potential. | cond-mat_dis-nn |
Spectral description of the dynamics of ultracold interacting bosons in
disordered lattices: We study the dynamics of a nonlinear one-dimensional disordered system from a
spectral point of view. The spectral entropy and the Lyapunov exponent are
extracted from the short time dynamics, and shown to give a pertinent
characterization of the different dynamical regimes. The chaotic and
self-trapped regimes are governed by log-normal laws whose origin is traced to
the exponential shape of the eigenstates of the linear problem. These
quantities satisfy scaling laws depending on the initial state and explain the
system behaviour at longer times. | cond-mat_dis-nn |
Creep motion of an elastic string in a random potential: We study the creep motion of an elastic string in a two dimensional pinning
landscape by Langevin dynamics simulations. We find that the Velocity-Force
characteristics are well described by the creep formula predicted from
phenomenological scaling arguments. We analyze the creep exponent $\mu$, and
the roughness exponent $\zeta$. Two regimes are identified: when the
temperature is larger than the strength of the disorder we find $\mu \approx
1/4$ and $\zeta \approx 2/3$, in agreement with the
quasi-equilibrium-nucleation picture of creep motion; on the contrary, lowering
enough the temperature, the values of $\mu$ and $\zeta$ increase showing a
strong violation of the latter picture. | cond-mat_dis-nn |
Analysis of Many-body Localization Landscapes and Fock Space Morphology
via Persistent Homology: We analyze functionals that characterize the distribution of eigenstates in
Fock space through a tool derived from algebraic topology: persistent homology.
Drawing on recent generalizations of the localization landscape applicable to
mid-spectrum eigenstates, we introduce several novel persistent homology
observables in the context of many-body localization that exhibit transitional
behavior near the critical point. We demonstrate that the persistent homology
approach to localization landscapes and, in general, functionals on the Fock
space lattice offer insights into the structure of eigenstates unobtainable by
traditional means. | cond-mat_dis-nn |
Structure and Relaxation Dynamics of a Colloidal Gel: Using molecular dynamics computer simulations we investigate the structural
and dynamical properties of a simple model for a colloidal gel at low volume
fraction. We find that at low T the system is forming an open percolating
cluster, without any sign of a phase separation. The nature of the relaxation
dynamics depends strongly on the length scale/wave-vector considered and can be
directly related to the geometrical properties of the spanning cluster. | cond-mat_dis-nn |
Probing tails of energy distributions using importance-sampling in the
disorder with a guiding function: We propose a simple and general procedure based on a recently introduced
approach that uses an importance-sampling Monte Carlo algorithm in the disorder
to probe to high precision the tails of ground-state energy distributions of
disordered systems. Our approach requires an estimate of the ground-state
energy distribution as a guiding function which can be obtained from
simple-sampling simulations. In order to illustrate the algorithm, we compute
the ground-state energy distribution of the Sherrington-Kirkpatrick mean-field
Ising spin glass to eighteen orders of magnitude. We find that the ground-state
energy distribution in the thermodynamic limit is well fitted by a modified
Gumbel distribution as previously predicted, but with a value of the slope
parameter m which is clearly larger than 6 and of the order 11. | cond-mat_dis-nn |
Statistical Properties of the one dimensional Anderson model relevant
for the Nonlinear Schrödinger Equation in a random potential: The statistical properties of overlap sums of groups of four eigenfunctions
of the Anderson model for localization as well as combinations of four
eigenenergies are computed. Some of the distributions are found to be scaling
functions, as expected from the scaling theory for localization. These enable
to compute the distributions in regimes that are otherwise beyond the
computational resources. These distributions are of great importance for the
exploration of the Nonlinear Schr\"odinger Equation (NLSE) in a random
potential since in some explorations the terms we study are considered as noise
and the present work describes its statistical properties. | cond-mat_dis-nn |
Tower of quantum scars in a partially many-body localized system: Isolated quantum many-body systems are often well-described by the eigenstate
thermalization hypothesis. There are, however, mechanisms that cause different
behavior: many-body localization and quantum many-body scars. Here, we show how
one can find disordered Hamiltonians hosting a tower of scars by adapting a
known method for finding parent Hamiltonians. Using this method, we construct a
spin-1/2 model which is both partially localized and contains scars. We
demonstrate that the model is partially localized by studying numerically the
level spacing statistics and bipartite entanglement entropy. As disorder is
introduced, the adjacent gap ratio transitions from the Gaussian orthogonal
ensemble to the Poisson distribution and the entropy shifts from volume-law to
area-law scaling. We investigate the properties of scars in a partially
localized background and compare with a thermal background. At strong disorder,
states initialized inside or outside the scar subspace display different
dynamical behavior but have similar entanglement entropy and Schmidt gap. We
demonstrate that localization stabilizes scar revivals of initial states with
support both inside and outside the scar subspace. Finally, we show how strong
disorder introduces additional approximate towers of eigenstates. | cond-mat_dis-nn |
Delocalization of topological surface states by diagonal disorder in
nodal loop semimetals: The effect of Anderson diagonal disorder on the topological surface
(``drumhead'') states of a Weyl nodal loop semimetal is addressed. Since
diagonal disorder breaks chiral symmetry, a winding number cannot be defined.
Seen as a perturbation, the weak random potential mixes the clean exponentially
localized drumhead states of the semimetal, thereby producing two effects: (i)
the algebraic decay of the surface states into the bulk; (ii) a broadening of
the low energy density of surface states of the open system due to degeneracy
lifting. This behavior persists with increasing disorder, up to the bulk
semimetal-to-metal transition at the critical disorder $W_{c}$. Above $W_{c}$,
the surface states hybridize with bulk states and become extended into the
bulk. | cond-mat_dis-nn |
Probing the dynamics of Anderson localization through spatial mapping: We study (1+1)D transverse localization of electromagnetic radiation at
microwave frequencies directly by two-dimensional spatial scans. Since the
longitudinal direction can be mapped onto time, our experiments provide unique
snapshots of the build-up of localized waves. The evolution of the wave
functions is compared with numerical calculations. Dissipation is shown to have
no effect on the occurrence of transverse localization. Oscillations of the
wave functions are observed in space and explained in terms of a beating
between the eigenstates. | cond-mat_dis-nn |
Supermetallic and Trapped States in Periodically Kicked Lattices: A periodically driven lattice with two commensurate spatial periodicities is
found to exhibit super metallic states characterized by enhancements in wave
packet spreading and entropy. These resonances occur at critical values of
parameters where multi-band dispersion curves reduce to a universal function
that is topologically a circle and the effective quantum dynamics describes
free propagation. Sandwiching every resonant state are a pair of anti-resonant
{\it trapped states} distinguished by dips in entropy where the transport, as
seen in the spreading rate, is only somewhat inhibited. Existing in gapless
phases fo the spectrum, a sequence of these peaks and dips are interspersed by
gapped phases assocated with flat band states where both the wave packet
spreading as well as the entropy exhibit local minima. | cond-mat_dis-nn |
Multifractality of ab initio wave functions in doped semiconductors: In Refs. [1,2] we have shown how a combination of modern linear-scaling DFT,
together with a subsequent use of large, effective tight-binding Hamiltonians,
allows to compute multifractal wave functions yielding the critical properties
of the Anderson metal-insulator transition (MIT) in doped semiconductors. This
combination allowed us to construct large and atomistically realistic samples
of sulfur-doped silicon (Si:S). The critical properties of such systems and the
existence of the MIT are well known, but experimentally determined values of
the critical exponent $\nu$ close to the transition have remained different
from those obtained by the standard tight-binding Anderson model. In Ref. [1],
we found that this ``exponent puzzle'' can be resolved when using our novel
\emph{ab initio} approach based on scaling of multifractal exponents in the
realistic impurity band for Si:S. Here, after a short review of
multifractality, we give details of the multifractal analysis as used in [1]
and show the obtained \emph{critical} multifractal spectrum at the MIT for
Si:S. | cond-mat_dis-nn |
Coexistence of localization and transport in many-body two-dimensional
Aubry-André models: Whether disordered and quasiperiodic many-body quantum systems host a
long-lived localized phase in the thermodynamic limit has been the subject of
intense recent debate. While in one dimension substantial evidence for the
existence of such a many-body localized (MBL) phase exists, the behavior in
higher dimensions remains an open puzzle. In two-dimensional disordered
systems, for instance, it has been argued that rare regions may lead to
thermalization of the whole system through a mechanism dubbed the avalanche
instability. In quasiperiodic systems, rare regions are altogether absent and
the fate of a putative many-body localized phase has hitherto remained largely
unexplored. In this work, we investigate the localization properties of two
many-body quasiperiodic models, which are two-dimensional generalizations of
the Aubry-Andr\'e model. By studying the out-of-equilibrium dynamics of large
systems, we find a long-lived MBL phase, in contrast to random systems.
Furthermore, we show that deterministic lines of weak potential, which appear
in investigated quasiperiodic models, support large-scale transport, while the
system as a whole does not thermalize. Our results demonstrate that
quasiperiodic many-body systems have the remarkable and counter-intuitive
capability of exhibiting coexisting localization and transport properties - a
phenomenon reminiscent of the behavior of supersolids. Our findings are of
direct experimental relevance and can be tested, for instance, using
state-of-the-art cold atomic systems. | cond-mat_dis-nn |
Failure Probabilities and Tough-Brittle Crossover of Heterogeneous
Materials with Continuous Disorder: The failure probabilities or the strength distributions of heterogeneous 1D
systems with continuous local strength distribution and local load sharing have
been studied using a simple, exact, recursive method. The fracture behavior
depends on the local bond-strength distribution, the system size, and the
applied stress, and crossovers occur as system size or stress changes. In the
brittle region, systems with continuous disorders have a failure probability of
the modified-Gumbel form, similar to that for systems with percolation
disorder. The modified-Gumbel form is of special significance in weak-stress
situations. This new recursive method has also been generalized to calculate
exactly the failure probabilities under various boundary conditions, thereby
illustrating the important effect of surfaces in the fracture process. | cond-mat_dis-nn |
Crossovers in ScaleFree Networks on Geographical Space: Complex networks are characterized by several topological properties: degree
distribution, clustering coefficient, average shortest path length, etc. Using
a simple model to generate scale-free networks embedded on geographical space,
we analyze the relationship between topological properties of the network and
attributes (fitness and location) of the vertices in the network. We find there
are two crossovers for varying the scaling exponent of the fitness
distribution. | cond-mat_dis-nn |
"Single Ring Theorem" and the Disk-Annulus Phase Transition: Recently, an analytic method was developed to study in the large $N$ limit
non-hermitean random matrices that are drawn from a large class of circularly
symmetric non-Gaussian probability distributions, thus extending the existing
Gaussian non-hermitean literature. One obtains an explicit algebraic equation
for the integrated density of eigenvalues from which the Green's function and
averaged density of eigenvalues could be calculated in a simple manner. Thus,
that formalism may be thought of as the non-hermitean analog of the method due
to Br\'ezin, Itzykson, Parisi and Zuber for analyzing hermitean non-Gaussian
random matrices. A somewhat surprising result is the so called "Single Ring"
theorem, namely, that the domain of the eigenvalue distribution in the complex
plane is either a disk or an annulus. In this paper we extend previous results
and provide simple new explicit expressions for the radii of the eigenvalue
distiobution and for the value of the eigenvalue density at the edges of the
eigenvalue distribution of the non-hermitean matrix in terms of moments of the
eigenvalue distribution of the associated hermitean matrix. We then present
several numerical verifications of the previously obtained analytic results for
the quartic ensemble and its phase transition from a disk shaped eigenvalue
distribution to an annular distribution. Finally, we demonstrate numerically
the "Single Ring" theorem for the sextic potential, namely, the potential of
lowest degree for which the "Single Ring" theorem has non-trivial consequences. | cond-mat_dis-nn |
Exact non-Hermitian mobility edges and robust flat bands in
two-dimensional Lieb lattices with imaginary quasiperiodic potentials: The mobility edge (ME) is a critical energy delineates the boundary between
extended and localized states within the energy spectrum, and it plays a
crucial role in understanding the metal-insulator transition in disordered or
quasiperiodic systems. While there have been extensive studies on MEs in
one-dimensional non-Hermitian (NH) quasiperiodic lattices recently, the
investigation of exact NH MEs in two-dimensional (2D) cases remains rare. In
the present study, we introduce a 2D dissipative Lieb lattice (DLL) model with
imaginary quasiperiodic potentials applied solely to the vertices of the Lieb
lattice. By mapping this DLL model to the 2D NH Aubry-Andr{\'e}-Harper (AAH)
model, we analytically derive the exact ME and find it associated with the
absolute eigenenergies. We find that the eigenvalues of extended states are
purely imaginary when the quasiperiodic potential is strong enough.
Additionally, we demonstrate that the introduction of imaginary quasiperiodic
potentials does not disrupt the flat bands inherent in the system. Finally, we
propose a theoretical framework for realizing our model using the Lindblad
master equation. Our results pave the way for further investigation of exact NH
MEs and flat bands in 2D dissipative quasiperiodic systems. | cond-mat_dis-nn |
Adaptive cluster expansion for the inverse Ising problem: convergence,
algorithm and tests: We present a procedure to solve the inverse Ising problem, that is to find
the interactions between a set of binary variables from the measure of their
equilibrium correlations. The method consists in constructing and selecting
specific clusters of variables, based on their contributions to the
cross-entropy of the Ising model. Small contributions are discarded to avoid
overfitting and to make the computation tractable. The properties of the
cluster expansion and its performances on synthetic data are studied. To make
the implementation easier we give the pseudo-code of the algorithm. | cond-mat_dis-nn |
Topology invariance in Percolation Thresholds: An universal invariant for site and bond percolation thresholds (p_{cs} and
p_{cb} respectively) is proposed. The invariant writes
{p_{cs}}^{1/a_s}{p_{cb}}^{-1/a_b}=\delta/d where a_s, a_b and \delta are
positive constants,and d the space dimension. It is independent of the
coordination number, thus exhibiting a topology invariance at any d.The formula
is checked against a large class of percolation problems, including percolation
in non-Bravais lattices and in aperiodic lattices as well as rigid percolation.
The invariant is satisfied within a relative error of \pm 5% for all the twenty
lattices of our sample at d=2, d=3, plus all hypercubes up to d=6. | cond-mat_dis-nn |
Exact Ground State Properties of Disordered Ising-Systems: Exact ground states are calculated with an integer optimization algorithm for
two and three dimensional site-diluted Ising antiferromagnets in a field (DAFF)
and random field Ising ferromagnets (RFIM). We investigate the structure and
the size-distribution of the domains of the ground state and compare it to
earlier results from Monte Carlo simulations for finite temperature. Although
DAFF and RFIM are thought to be in the same universality class we found
essential differences between these systems as far as the domain properties are
concerned. For the DAFF the ground states consist of fractal domains with a
broad size distribution that can be described by a power law with exponential
cut-off. For the RFIM the limiting case of the size distribution and structure
of the domains for strong random fields is the size distribution and structure
of the clusters of the percolation problem with a field dependent lower
cut-off. The domains are fractal and in three dimensions nearly all spins
belong to two large infinite domains of up- and down spins - the system is in a
two-domain state. | cond-mat_dis-nn |
Towards quantization Conway Game of Life: Classical stochastic Conway Game of Life is expressed by the dissipative
Schr\"odinger equation and dissipative tight-binding model. This is conducted
at the prize of usage of time dependent anomalous non-Hermitian Hamiltonians as
with occurrence of complex value potential that do not preserve the
normalization of wave-function and thus allows for mimicking creationism or
annihilationism of cellular automaton. Simply saying time-dependent complex
value eigenenergies are similar to complex values of resonant frequencies in
electromagnetic resonant cavities reflecting presence of dissipation that
reflects energy leaving the system or being pumped into the system. At the same
time various aspects of thermodynamics were observed in cellular automata that
can be later reformulated by quantum mechanical pictures. The usage of Shannon
entropy and mass equivalence to energy points definition of cellular automata
temperature. Contrary to intuitive statement the system dynamical equilibrium
is always reflected by negative temperatures. Diffusion of mass, energy and
temperature as well as phase of proposed wave function is reported and can be
directly linked with second thermodynamics law approximately valid for the
system, where neither mass nor energy is conserved. The concept of
complex-valued mass mimics wave-function behavior. Equivalence an anomalous
second Fick law and dissipative Schr\"odinger equation is given. Dissipative
Conway Game of Life tight-binding Hamiltonian is given using phenomenological
justification. | cond-mat_dis-nn |
Effect of Strong Disorder on 3-Dimensional Chiral Topological
Insulators: Phase Diagrams, Maps of the Bulk Invariant and Existence of
Topological Extended Bulk States: The effect of strong disorder on chiral-symmetric 3-dimensional lattice
models is investigated via analytical and numerical methods. The phase diagrams
of the models are computed using the non-commutative winding number, as
functions of disorder strength and model's parameters. The
localized/delocalized characteristic of the quantum states is probed with level
statistics analysis. Our study re-confirms the accurate quantization of the
non-commutative winding number in the presence of strong disorder, and its
effectiveness as a numerical tool. Extended bulk states are detected above and
below the Fermi level, which are observed to undergo the so called "levitation
and pair annihilation" process when the system is driven through a topological
transition. This suggests that the bulk invariant is carried by these extended
states, in stark contrast with the 1-dimensional case where the extended states
are completely absent and the bulk invariant is carried by the localized
states. | cond-mat_dis-nn |
Interdependent networks with correlated degrees of mutually dependent
nodes: We study a problem of failure of two interdependent networks in the case of
correlated degrees of mutually dependent nodes. We assume that both networks (A
and B) have the same number of nodes $N$ connected by the bidirectional
dependency links establishing a one-to-one correspondence between the nodes of
the two networks in a such a way that the mutually dependent nodes have the
same number of connectivity links, i.e. their degrees coincide. This implies
that both networks have the same degree distribution $P(k)$. We call such
networks correspondently coupled networks (CCN). We assume that the nodes in
each network are randomly connected. We define the mutually connected clusters
and the mutual giant component as in earlier works on randomly coupled
interdependent networks and assume that only the nodes which belong to the
mutual giant component remain functional. We assume that initially a $1-p$
fraction of nodes are randomly removed due to an attack or failure and find
analytically, for an arbitrary $P(k)$, the fraction of nodes $\mu(p)$ which
belong to the mutual giant component. We find that the system undergoes a
percolation transition at certain fraction $p=p_c$ which is always smaller than
the $p_c$ for randomly coupled networks with the same $P(k)$. We also find that
the system undergoes a first order transition at $p_c>0$ if $P(k)$ has a finite
second moment. For the case of scale free networks with $2<\lambda \leq 3$, the
transition becomes a second order transition. Moreover, if $\lambda<3$ we find
$p_c=0$ as in percolation of a single network. For $\lambda=3$ we find an exact
analytical expression for $p_c>0$. Finally, we find that the robustness of CCN
increases with the broadness of their degree distribution. | cond-mat_dis-nn |
Memory effects in transport through a hopping insulator: Understanding
two-dip experiments: We discuss memory effects in the conductance of hopping insulators due to
slow rearrangements of many-electron clusters leading to formation of polarons
close to the electron hopping sites. An abrupt change in the gate voltage and
corresponding shift of the chemical potential change populations of the hopping
sites, which then slowly relax due to rearrangements of the clusters. As a
result, the density of hopping states becomes time dependent on a scale
relevant to rearrangement of the structural defects leading to the excess time
dependent conductivity. | cond-mat_dis-nn |
Long-range correlations of density in a Bose-Einstein condensate
expanding in a random potential: We study correlations of atomic density in a weakly interacting Bose-Einstein
condensate, expanding diffusively in a random potential. We show that these
correlations are long-range and that they are strongly enhanced at long times.
Density at distant points exhibits negative correlations. | cond-mat_dis-nn |
Many-body localization, thermalization, and entanglement: Thermalizing quantum systems are conventionally described by statistical
mechanics at equilibrium. However, not all systems fall into this category,
with many body localization providing a generic mechanism for thermalization to
fail in strongly disordered systems. Many-body localized (MBL) systems remain
perfect insulators at non-zero temperature, which do not thermalize and
therefore cannot be described using statistical mechanics. In this Colloquium
we review recent theoretical and experimental advances in studies of MBL
systems, focusing on the new perspective provided by entanglement and
non-equilibrium experimental probes such as quantum quenches. Theoretically,
MBL systems exhibit a new kind of robust integrability: an extensive set of
quasi-local integrals of motion emerges, which provides an intuitive
explanation of the breakdown of thermalization. A description based on
quasi-local integrals of motion is used to predict dynamical properties of MBL
systems, such as the spreading of quantum entanglement, the behavior of local
observables, and the response to external dissipative processes. Furthermore,
MBL systems can exhibit eigenstate transitions and quantum orders forbidden in
thermodynamic equilibrium. We outline the current theoretical understanding of
the quantum-to-classical transition between many-body localized and ergodic
phases, and anomalous transport in the vicinity of that transition.
Experimentally, synthetic quantum systems, which are well-isolated from an
external thermal reservoir, provide natural platforms for realizing the MBL
phase. We review recent experiments with ultracold atoms, trapped ions,
superconducting qubits, and quantum materials, in which different signatures of
many-body localization have been observed. We conclude by listing outstanding
challenges and promising future research directions. | cond-mat_dis-nn |
Anderson localization of a Bose-Einstein condensate in a 3D random
potential: We study the effect of Anderson localization on the expansion of a
Bose-Einstein condensate, released from a harmonic trap, in a 3D random
potential. We use scaling arguments and the self-consistent theory of
localization to show that the long-time behavior of the condensate density is
controlled by a single parameter equal to the ratio of the mobility edge and
the chemical potential of the condensate. We find that the two critical
exponents of the localization transition determine the evolution of the
condensate density in time and space. | cond-mat_dis-nn |
Dimensional Dependence of Critical Exponent of the Anderson Transition
in the Orthogonal Universality Class: We report improved numerical estimates of the critical exponent of the
Anderson transition in Anderson's model of localization in $d=4$ and $d=5$
dimensions. We also report a new Borel-Pad\'e analysis of existing $\epsilon$
expansion results that incorporates the asymptotic behaviour for $d\to \infty$
and gives better agreement with available numerical results. | cond-mat_dis-nn |
Phase Transition in the Random Anisotropy Model: The influence of a local anisotropy of random orientation on a ferromagnetic
phase transition is studied for two cases of anisotropy axis distribution. To
this end a model of a random anisotropy magnet is analyzed by means of the
field theoretical renormalization group approach in two loop approximation
refined by a resummation of the asymptotic series. The one-loop result of
Aharony indicating the absence of a second-order phase transition for an
isotropic distribution of random anisotropy axis at space dimension $d<4$ is
corroborated. For a cubic distribution the accessible stable fixed point leads
to disordered Ising-like critical exponents. | cond-mat_dis-nn |
Universality and universal finite-size scaling functions in
four-dimensional Ising spin glasses: We study the four-dimensional Ising spin glass with Gaussian and bond-diluted
bimodal distributed interactions via large-scale Monte Carlo simulations and
show via an extensive finite-size scaling analysis that four-dimensional Ising
spin glasses obey universality. | cond-mat_dis-nn |
From power law to Anderson localization in nonlinear Schrödinger
equation with nonlinear randomness: We study the propagation of coherent waves in a nonlinearly-induced random
potential, and find regimes of self-organized criticality and other regimes
where the nonlinear equivalent of Anderson localization prevails. The regime of
self-organized criticality leads to power-law decay of transport [Phys. Rev.
Lett. 121, 233901 (2018)], whereas the second regime exhibits exponential
decay. | cond-mat_dis-nn |
The Leontovich boundary conditions and calculation of effective
impedance of inhomogeneous metal: We bring forward rather simple algorithm allowing us to calculate the
effective impedance of inhomogeneous metals in the frequency region where the
local Leontovich (the impedance) boundary conditions are justified. The
inhomogeneity is due to the properties of the metal or/and the surface
roughness. Our results are nonperturbative ones with respect to the
inhomogeneity amplitude. They are based on the recently obtained exact result
for the effective impedance of inhomogeneous metals with flat surfaces.
One-dimension surfaces inhomogeneities are examined. Particular attention is
paid to the influence of generated evanescent waves on the reflection
characteristics. We show that if the surface roughness is rather strong, the
element of the effective impedance tensor relating to the p- polarization state
is much greater than the input local impedance. As examples, we calculate: i)
the effective impedance for a flat surface with strongly nonhomogeneous
periodic strip-like local impedance; ii) the effective impedance associated
with one-dimensional lamellar grating. For the problem (i) we also present
equations for the forth lines of the Pointing vector in the vicinity of the
surface. | cond-mat_dis-nn |
Comment on "Erratum: Collective modes and gapped momentum states in
liquid Ga:Experiment, theory, and simulation": We show, that the theoretical expression for the dispersion of collective
excitations reported in [Phys. Rev. B {\bf 103}, 099901 (2021)], at variance
with what was claimed in the paper, does not account for the energy
fluctuations and does not tend in the long-wavelegth limit to the correct
hydrodynamic dispersion law. | cond-mat_dis-nn |
Quantum transport of atomic matterwaves in anisotropic 2D and 3D
disorder: The macroscopic transport properties in a disordered potential, namely
diffusion and weak/strong localization, closely depend on the microscopic and
statistical properties of the disorder itself. This dependence is rich of
counter-intuitive consequences. It can be particularly exploited in matter wave
experiments, where the disordered potential can be tailored and controlled, and
anisotropies are naturally present. In this work, we apply a perturbative
microscopic transport theory and the self-consistent theory of Anderson
localization to study the transport properties of ultracold atoms in
anisotropic 2D and 3D speckle potentials. In particular, we discuss the
anisotropy of single-scattering, diffusion and localization. We also calculate
a disorder-induced shift of the energy states and propose a method to include
it, which amounts to renormalize energies in the standard on-shell
approximation. We show that the renormalization of energies strongly affects
the prediction for the 3D localization threshold (mobility edge). We illustrate
the theoretical findings with examples which are revelant for current matter
wave experiments, where the disorder is created with a laser speckle. This
paper provides a guideline for future experiments aiming at the precise
location of the 3D mobility edge and study of anisotropic diffusion and
localization effects in 2D and 3D. | cond-mat_dis-nn |
Elementary plastic events in amorphous silica: Plastic instabilities in amorphous materials are often studied using
idealized models of binary mixtures that do not capture accurately molecular
interactions and bonding present in real glasses. Here we study atomic scale
plastic instabilities in a three dimensional molecular dynamics model of silica
glass under quasi-static shear. We identify two distinct types of elementary
plastic events, one is a standard quasi-localized atomic rearrangement while
the second is a bond breaking event that is absent in simplified models of
fragile glass formers. Our results show that both plastic events can be
predicted by a drop of the lowest non-zero eigenvalue of the Hessian matrix
that vanishes at a critical strain. Remarkably, we find very high correlation
between the associated eigenvectors and the non-affine displacement fields
accompanying the bond breaking event, predicting the locus of structural
failure. Both eigenvectors and non-affine displacement fields display an
Eshelby-like quadrupolar structure for both failure modes, rearrangement or
bond-breaking. Our results thus clarify the nature of atomic scale plastic
instabilities in silica glasses providing useful information for the
development of mesoscale models of amorphous plasticity. | cond-mat_dis-nn |
Correlated Domains in Spin Glasses: We study the 3D Edwards-Anderson spin glasses, by analyzing spin-spin
correlation functions in thermalized spin configurations at low T on large
lattices. We consider individual disorder samples and analyze connected
clusters of very correlated sites: we analyze how the volume and the surface of
these clusters increases with the lattice size. We qualify the important
excitations of the system by checking how large they are, and we define a
correlation length by measuring their gyration radius. We find that the
clusters have a very dense interface, compatible with being space filling. | cond-mat_dis-nn |
Probing many-body localization in a disordered quantum magnet: Quantum states cohere and interfere. Quantum systems composed of many atoms
arranged imperfectly rarely display these properties. Here we demonstrate an
exception in a disordered quantum magnet that divides itself into nearly
isolated subsystems. We probe these coherent clusters of spins by driving the
system beyond its linear response regime at a single frequency and measuring
the resulting "hole" in the overall linear spectral response. The Fano shape of
the hole encodes the incoherent lifetime as well as coherent mixing of the
localized excitations. For the disordered Ising magnet,
$\mathrm{LiHo_{0.045}Y_{0.955}F_4}$, the quality factor $Q$ for spectral holes
can be as high as 100,000. We tune the dynamics of the quantum degrees of
freedom by sweeping the Fano mixing parameter $q$ through zero via the
amplitude of the ac pump as well as a static external transverse field. The
zero-crossing of $q$ is associated with a dissipationless response at the drive
frequency, implying that the off-diagonal matrix element for the two-level
system also undergoes a zero-crossing. The identification of localized
two-level systems in a dense and disordered dipolar-coupled spin system
represents a solid state implementation of many-body localization, pushing the
search forward for qubits emerging from strongly-interacting, disordered,
many-body systems. | cond-mat_dis-nn |
Novel scaling behavior of the Ising model on curved surfaces: We demonstrate the nontrivial scaling behavior of Ising models defined on (i)
a donut-shaped surface and (ii) a curved surface with a constant negative
curvature. By performing Monte Carlo simulations, we find that the former model
has two distinct critical temperatures at which both the specific heat $C(T)$
and magnetic susceptibility $\chi(T)$ show sharp peaks.The critical exponents
associated with the two critical temperatures are evaluated by the finite-size
scaling analysis; the result reveals that the values of these exponents vary
depending on the temperature range under consideration. In the case of the
latter model, it is found that static and dynamic critical exponents deviate
from those of the Ising model on a flat plane; this is a direct consequence of
the constant negative curvature of the underlying surface. | cond-mat_dis-nn |
Reply to Comment on "Quantum Phase Transition of Randomly-Diluted
Heisenberg Antiferromagnet on a Square Lattice": This is a reply to the comment by A. W. Sandvik (cond-mat/0010433) on our
paper Phys. Rev. Lett. 84, 4204 (2000). We show that his data do not conflict
with our data nor with our conclusions. | cond-mat_dis-nn |
Realization-dependent model of hopping transport in disordered media: At low injection or low temperatures, electron transport in disordered
semiconductors is dominated by phonon-assisted hopping between localized
states. A very popular approach to this hopping transport is the
Miller-Abrahams model that requires a set of empirical parameters to define the
hopping rates and the preferential paths between the states. We present here a
transport model based on the localization landscape (LL) theory in which the
location of the localized states, their energies, and the coupling between them
are computed for any specific realization, accounting for its particular
geometry and structure. This model unveils the transport network followed by
the charge carriers that essentially consists in the geodesics of a metric
deduced from the LL. The hopping rates and mobility are computed on a
paradigmatic example of disordered semiconductor, and compared with the
prediction from the actual solution of the Schr\"odinger equation. We explore
the temperature-dependency for various disorder strengths and demonstrate the
applicability of the LL theory in efficiently modeling hopping transport in
disordered systems. | cond-mat_dis-nn |
A theory of π/2 superconducting Josephson junctions: We consider theoretically a Josephson junction with a superconducting
critical current density which has a random sign along the junction's surface.
We show that the ground state of the junction corresponds to the phase
difference equal to \pi/2. Such a situation can take place in superconductor-
ferromagnet junction. | cond-mat_dis-nn |
Extended states in disordered systems: role of off-diagonal correlations: We study one-dimensional systems with random diagonal disorder but
off-diagonal short-range correlations imposed by structural constraints. We
find that these correlations generate effective conduction channels for finite
systems. At a certain golden correlation condition for the hopping amplitudes,
we find an extended state for an infinite system. Our model has important
implications to charge transport in DNA molecules, and a possible set of
experiments in semiconductor superlattices is proposed to verify our most
interesting theoretical predictions. | cond-mat_dis-nn |
Real space Renormalization Group analysis of a non-mean field spin-glass: A real space Renormalization Group approach is presented for a non-mean field
spin-glass. This approach has been conceived in the effort to develop an
alternative method to the Renormalization Group approaches based on the replica
method. Indeed, non-perturbative effects in the latter are quite generally out
of control, in such a way that these approaches are non-predictive. On the
contrary, we show that the real space method developed in this work yields
precise predictions for the critical behavior and exponents of the model. | cond-mat_dis-nn |
Signature of ballistic effects in disordered conductors: Statistical properties of energy levels, wave functions and
quantum-mechanical matrix elements in disordered conductors are usually
calculated assuming diffusive electron dynamics. Mirlin has pointed out [Phys.
Rep. 326, 259 (2000)] that ballistic effects may, under certain circumstances,
dominate diffusive contributions. We study the influence of such ballistic
effects on the statistical properties of wave functions in quasi-one
dimensional disordered conductors. Our results support the view that ballistic
effects can be significant in these systems. | cond-mat_dis-nn |
Democratic particle motion for meta-basin transitions in simple
glass-formers: We use molecular dynamics computer simulations to investigate the local
motion of the particles in a supercooled simple liquid. Using the concept of
the distance matrix we find that the alpha-relaxation corresponds to a small
number of crossings from one meta-basin to a neighboring one. Each crossing is
very rapid and involves the collective motion of O(40) particles that form a
relatively compact cluster, whereas string-like motions seem not to be relevant
for these transitions. These compact clusters are thus candidates for the
cooperatively rearranging regions proposed long times ago by Adam and Gibbs. | cond-mat_dis-nn |
Resistance distance distribution in large sparse random graphs: We consider an Erdos-Renyi random graph consisting of N vertices connected by
randomly and independently drawing an edge between every pair of them with
probability c/N so that at N->infinity one obtains a graph of finite mean
degree c. In this regime, we study the distribution of resistance distances
between the vertices of this graph and develop an auxiliary field
representation for this quantity in the spirit of statistical field theory.
Using this representation, a saddle point evaluation of the resistance distance
distribution is possible at N->infinity in terms of an 1/c expansion. The
leading order of this expansion captures the results of numerical simulations
very well down to rather small values of c; for example, it recovers the
empirical distribution at c=4 or 6 with an overlap of around 90%. At large
values of c, the distribution tends to a Gaussian of mean 2/c and standard
deviation sqrt{2/c^3}. At small values of c, the distribution is skewed toward
larger values, as captured by our saddle point analysis, and many fine features
appear in addition to the main peak, including subleading peaks that can be
traced back to resistance distances between vertices of specific low degrees
and the rest of the graph. We develop a more refined saddle point scheme that
extracts the corresponding degree-differentiated resistance distance
distributions. We then use this approach to recover analytically the most
apparent of the subleading peaks that originates from vertices of degree 1.
Rather intuitively, this subleading peak turns out to be a copy of the main
peak, shifted by one unit of resistance distance and scaled down by the
probability for a vertex to have degree 1. We comment on a possible lack of
smoothness in the true N->infinity distribution suggested by the numerics. | cond-mat_dis-nn |
Sensitivity, Itinerancy and Chaos in Partly-Synchronized Weighted
Networks: We present exact results, as well as some illustrative Monte Carlo
simulations, concerning a stochastic network with weighted connections in which
the fraction of nodes that are dynamically synchronized is a parameter. This
allows one to describe from single-node kinetics to simultaneous updating of
all the variables at each time unit. An example of the former limit is the
well-known sequential updating of spins in kinetic magnetic models whereas the
latter limit is common for updating complex cellular automata. The emergent
behavior changes dramatically as the parameter is varied. For small values, we
observed relaxation towards one of the attractors and a great sensibility to
external stimuli, and for large synchronization, itinerancy as in heteroclinic
paths among attractors; tuning the parameter in this regime, the oscillations
with time may abruptly change from regular to chaotic and vice versa. We show
how these observations, which may be relevant concerning computational
strategies, closely resemble some actual situations related to both searching
and states of attention in the brain. | cond-mat_dis-nn |
Modelling Quasicrystal Growth: Understanding the growth of quasicrystals poses a challenging problem, not
the least because the quasiperiodic order present in idealized mathematical
models of quasicrystals prohibit simple local growth algorithms. This can only
be circumvented by allowing for some degree of disorder, which of course is
always present in real quasicrystalline samples. In this review, we give an
overview of the present state of theoretical research, addressing the problems,
the different approaches and the results obtained so far. | cond-mat_dis-nn |
Electric field induced memory and aging effects in pure solid N_2: We report combined high sensitivity dielectric constant and heat capacity
measurements of pure solid N_2 in the presence of a small external ac electric
field in the audio frequency range. We have observed strong field induced aging
and memory effects which show that field cooled samples may be prepared in a
variety of metastable states leading to a free energy landscape with
experimentally ``tunable'' barriers, and tunneling between these states may
occur within laboratory time scales. | cond-mat_dis-nn |
Criterion for the occurrence of many body localization in the presence
of a single particle mobility edge: Non-interacting fermions in one dimension can undergo a
localization-delocalization transition in the presence of a quasi-periodic
potential as a function of that potential. In the presence of interactions,
this transition transforms into a Many-Body Localization (MBL) transition.
Recent studies have suggested that this type of transition can also occur in
models with quasi-periodic potentials that possess single particle mobility
edges. Two such models were studied in PRL 115,230401(2015) but only one was
found to exhibit an MBL transition in the presence of interactions while the
other one did not. In this work we investigate the occurrence of MBL in the
presence of weak interactions in five different models with single particle
mobility edges in one dimension with a view to obtaining a criterion for the
same. We find that not all such models undergo a thermal-MBL phase transition
in presence of weak interactions. We propose a criterion to determine whether
MBL is likely to occur in presence of interaction based only on the properties
of the non-interacting models. The relevant quantity $\epsilon$ is a measure of
how localized the localized states are relative to how delocalized the
delocalized states are in the non-interacting model. We also study various
other features of the non-interacting models such as the divergence of the
localization length at the mobility edge and the presence or absence of
`ergodicity' and localization in their many-body eigenstates. However, we find
that these features cannot be used to predict the occurrence of MBL upon the
introduction of weak interactions. | cond-mat_dis-nn |
Numerical evidences of a universal critical behavior of 2D and 3D random
quantum clock and Potts models: The random quantum $q$-state clock and Potts models are studied in 2 and 3
dimensions. The existence of Griffiths phases is tested in the 2D case with
$q=6$ by sampling the integrated probability distribution of local
susceptibilities of the equivalent McCoy-Wu 3D classical modelswith Monte Carlo
simulations. No Griffiths phase is found for the clock model. In contrast,
numerical evidences of the existence of Griffiths phases in the random Potts
model are given and the Finite Size effects are analyzed. The critical point of
the random quantum clock model is then studied by Strong-Disorder
Renormalization Group. Despite a chaotic behavior of the Renormalization-Group
flow at weak disorder, evidences are given that this critical behavior is
governed by the same Infinite-Disorder Fixed Point as the Potts model,
independently from the number of states $q$. | cond-mat_dis-nn |
Absence of disordered Thouless pumps at finite frequency: A Thouless pump is a slowly driven one-dimensional band insulator which pumps
charge at a quantised rate. Previous work showed that pumping persists in
weakly disordered chains, and separately in clean chains at finite drive
frequency. We study the interplay of disorder and finite frequency, and show
that the pump rate always decays to zero due to non-adiabatic transitions
between the instantaneous eigenstates. However, the decay is slow, occurring on
a time-scale that is exponentially large in the period of the drive. In the
adiabatic limit, the band gap in the instantaneous spectrum closes at a
critical disorder strength above which pumping ceases. We predict the scaling
of the pump rate around this transition from a model of scattering between rare
states near the band edges. Our predictions can be experimentally tested in
ultracold atomic and photonic platforms. | cond-mat_dis-nn |
Frequency propagation: Multi-mechanism learning in nonlinear physical
networks: We introduce frequency propagation, a learning algorithm for nonlinear
physical networks. In a resistive electrical circuit with variable resistors,
an activation current is applied at a set of input nodes at one frequency, and
an error current is applied at a set of output nodes at another frequency. The
voltage response of the circuit to these boundary currents is the superposition
of an `activation signal' and an `error signal' whose coefficients can be read
in different frequencies of the frequency domain. Each conductance is updated
proportionally to the product of the two coefficients. The learning rule is
local and proved to perform gradient descent on a loss function. We argue that
frequency propagation is an instance of a multi-mechanism learning strategy for
physical networks, be it resistive, elastic, or flow networks. Multi-mechanism
learning strategies incorporate at least two physical quantities, potentially
governed by independent physical mechanisms, to act as activation and error
signals in the training process. Locally available information about these two
signals is then used to update the trainable parameters to perform gradient
descent. We demonstrate how earlier work implementing learning via chemical
signaling in flow networks also falls under the rubric of multi-mechanism
learning. | cond-mat_dis-nn |
Solvable model of a polymer in random media with long ranged disorder
correlations: We present an exactly solvable model of a Gaussian (flexible) polymer chain
in a quenched random medium. This is the case when the random medium obeys very
long range quadratic correlations. The model is solved in $d$ spatial
dimensions using the replica method, and practically all the physical
properties of the chain can be found. In particular the difference between the
behavior of a chain that is free to move and a chain with one end fixed is
elucidated. The interesting finding is that a chain that is free to move in a
quadratically correlated random potential behaves like a free chain with $R^2
\sim L$, where $R$ is the end to end distance and $L$ is the length of the
chain, whereas for a chain anchored at one end $R^2 \sim L^4$. The exact
results are found to agree with an alternative numerical solution in $d=1$
dimensions. The crossover from long ranged to short ranged correlations of the
disorder is also explored. | cond-mat_dis-nn |
Floquet Time Crystals: We define what it means for time translation symmetry to be spontaneously
broken in a quantum system, and show with analytical arguments and numerical
simulations that this occurs in a large class of many-body-localized driven
systems with discrete time-translation symmetry. | cond-mat_dis-nn |
Zero-temperature Glauber dynamics on small-world networks: The zero-temperature Glauber dynamics of the ferromagnetic Ising model on
small-world networks, rewired from a two-dimensional square lattice, has been
studied by numerical simulations. For increasing disorder in finite networks,
the nonequilibrium dynamics becomes faster, so that the ground state is found
more likely. For any finite value of the rewiring probability p, the likelihood
of reaching the ground state goes to zero in the thermodynamic limit, similarly
to random networks. The spin correlation xi(r) is found to decrease with
distance as xi(r) ~ exp(-r/lambda), lambda being a correlation length scaling
with p as lambda ~ p^(-0.73). These results are compared with those obtained
earlier for addition-type small world networks. | cond-mat_dis-nn |
Scaling the alpha-relaxation time of supercooled fragile organic liquids: It was shown recently that the structural alpha-relaxation time tau of
supercooled o-terphenyl depends on a single control parameter Gamma, which is
the product of a function of density E(ro), by the inverse temperature T -1. We
extend this finding to other fragile glassforming liquids using
light-scattering data. Available experimental results do not allow to
discriminate between several analytical forms of the function E(ro), the
scaling arising from the separation of density and temperature in Gamma. We
also propose a simple form for tau(Gamma), which depends only on three
material-dependent parameters, reproducing relaxation times over 12 orders of
magnitude. | cond-mat_dis-nn |
Rare region effects and dynamics near the many-body localization
transition: The low-frequency response of systems near the many-body localization phase
transition, on either side of the transition, is dominated by contributions
from rare regions that are locally "in the other phase", i.e., rare localized
regions in a system that is typically thermal, or rare thermal regions in a
system that is typically localized. Rare localized regions affect the
properties of the thermal phase, especially in one dimension, by acting as
bottlenecks for transport and the growth of entanglement, whereas rare thermal
regions in the localized phase act as local "baths" and dominate the
low-frequency response of the MBL phase. We review recent progress in
understanding these rare-region effects, and discuss some of the open questions
associated with them: in particular, whether and in what circumstances a single
rare thermal region can destabilize the many-body localized phase. | cond-mat_dis-nn |
Human Genome data analyzed by an evolutionary method suggests a decrease
in cerebral protein-synthesis rate as cause of schizophrenia and an increase
as antipsychotic mechanism: The Human Genome Project (HGP) provides researchers with the data of nearly
all human genes and the challenge to use this information for elucidating the
etiology of common disorders. A secondary Darwinian method was applied to HGP
and other research data to approximate and possibly unravel the etiology of
schizophrenia. The results indicate that genetic and epigenetic variants of
genes involved in signal transduction, transcription and translation -
converging at the protein-synthesis rate (PSR) as common final pathway - might
be responsible for the genetic susceptibility to schizophrenia. Environmental
(e.g. viruses)and/or genetic factors can lead to cerebral PSR (CPSR)
deficiency. The CPSR hypothesis of schizophrenia and antipsychotic mechanism
explains 96% of the major facts of schizophrenia, reveals links between
previously unrelated facts, integrates many hypotheses, and implies that
schizophrenia should be easily preventable and treatable, partly by
immunization against neurotrophic viruses and partly by the development of new
drugs which selectively increase CPSR. Part of the manuscript has been
published in a modified form as "The glial growth factors deficiency and
synaptic destabilization hypothesis of schizophrenia" in BMC Psychiatry
available online at http://www.biomedcentral.com/1471-244X/2/8/ | cond-mat_dis-nn |
Critical-to-Insulator Transitions and Fractality Edges in Perturbed
Flatbands: We study the effect of quasiperiodic perturbations on one-dimensional
all-bands-flat lattice models. Such networks can be diagonalized by a finite
sequence of local unitary transformations parameterized by angles $\theta_i$.
Without loss of generality, we focus on the case of two bands with bandgap
$\Delta$. Weak perturbations lead to an effective Hamiltonian with both on- and
off-diagonal quasiperiodic terms that depend on $\theta_i$. For some angle
values, the effective model coincides with the extended Harper model. By
varying the parameters of the quasiperiodic potentials, \iffalse and the
manifold angles $\theta_i$ \fi we observe localized insulating states and an
entire parameter range hosting critical states with subdiffusive transport. For
finite quasiperiodic potential strength, the critical-to-insulating transition
becomes energy dependent with what we term fractality edges separating
localized from critical states. | cond-mat_dis-nn |
Dynamic entropies, long-range correlations, and fluctuations in complex
linear structures: We investigate symbolic sequences and in particular information carriers as
e.g. books and DNA-strings. First the higher order Shannon entropies are
calculated, a characteristic root law is detected. Then the algorithmic entropy
is estimated by using Lempel-Ziv compression algorithms. In the third section
the correlation function for distant letters, the low frequency Fourier
spectrum and the characteristic scaling exponents are calculated. We show that
all these measures are able to detect long-range correlations. However, as
demonstrated by shuffling experiments, different measures operate on different
length scales. The longest correlations found in our analysis comprise a few
hundreds or thousands of letters and may be understood as long-wave
fluctuations of the composition. | cond-mat_dis-nn |
Flat bands in fractal-like geometry: We report the presence of multiple flat bands in a class of two-dimensional
(2D) lattices formed by Sierpinski gasket (SPG) fractal geometries as the basic
unit cells. Solving the tight-binding Hamiltonian for such lattices with
different generations of a SPG network, we find multiple degenerate and
non-degenerate completely flat bands, depending on the configuration of
parameters of the Hamiltonian. Moreover, we find a generic formula to determine
the number of such bands as a function of the generation index $\ell$ of the
fractal geometry. We show that the flat bands and their neighboring dispersive
bands have remarkable features, the most interesting one being the spin-1
conical-type spectrum at the band center without any staggered magnetic flux,
in contrast to the Kagome lattice. We furthermore investigate the effect of the
magnetic flux in these lattice settings and show that different combinations of
fluxes through such fractal unit cells lead to richer spectrum with a single
isolated flat band or gapless electron- or hole-like flat bands. Finally, we
discuss a possible experimental setup to engineer such fractal flat band
network using single-mode laser-induced photonic waveguides. | cond-mat_dis-nn |
Localization in Correlated Bi-Layer Structures: From Photonic Cristals
to Metamaterials and Electron Superlattices: In a unified approach, we study the transport properties of
periodic-on-average bi-layered photonic crystals, metamaterials and electron
superlattices. Our consideration is based on the analytical expression for the
localization length derived for the case of weakly fluctuating widths of
layers, that also takes into account possible correlations in disorder. We
analyze how the correlations lead to anomalous properties of transport. In
particular, we show that for quarter stack layered media specific correlations
can result in a $\omega^2$-dependence of the Lyapunov exponent in all spectral
bands. | cond-mat_dis-nn |
Random Defect Lines in Conformal Minimal Models: We analyze the effect of adding quenched disorder along a defect line in the
2D conformal minimal models using replicas. The disorder is realized by a
random applied magnetic field in the Ising model, by fluctuations in the
ferromagnetic bond coupling in the Tricritical Ising model and Tricritical
Three-state Potts model (the $\phi_{12}$ operator), etc.. We find that for the
Ising model, the defect renormalizes to two decoupled half-planes without
disorder, but that for all other models, the defect renormalizes to a
disorder-dominated fixed point. Its critical properties are studied with an
expansion in $\eps \propto 1/m$ for the mth Virasoro minimal model. The decay
exponents $X_N=\frac{N}{2}(1-\frac{9(3N-4)}{4(m+1)^2}+
\mathcal{O}(\frac{3}{m+1})^3)$ of the Nth moment of the two-point function of
$\phi_{12}$ along the defect are obtained to 2-loop order, exhibiting
multifractal behavior.This leads to a typical decay exponent $X_{\rm typ}={1/2}
(1+\frac{9}{(m+1)^2}+\mathcal{O}(\frac{3}{m+1})^3)$. One-point functions are
seen to have a non-self-averaging amplitude. The boundary entropy is larger
than that of the pure system by order 1/m^3.
As a byproduct of our calculations, we also obtain to 2-loop order the
exponent $\tilde{X}_N=N(1-\frac{2}{9\pi^2}(3N-4)(q-2)^2+\mathcal{O}(q-2)^3)$ of
the Nth moment of the energy operator in the q-state Potts model with bulk bond
disorder. | cond-mat_dis-nn |
Simulating Spin Waves in Entropy Stabilized Oxides: The entropy stabilized oxide
Mg$_{0.2}$Co$_{0.2}$Ni$_{0.2}$Cu$_{0.2}$Zn$_{0.2}$O exhibits antiferromagnetic
order and magnetic excitations, as revealed by recent neutron scattering
experiments. This observation raises the question of the nature of spin wave
excitations in such disordered systems. Here, we investigate theoretically the
magnetic ground state and the spin-wave excitations using linear spin-wave
theory in combination with the supercell approximation to take into account the
extreme disorder in this magnetic system. We find that the experimentally
observed antiferromagnetic structure can be stabilized by a rhombohedral
distortion together with large second nearest neighbor interactions. Our
calculations show that the spin-wave spectrum consists of a well-defined
low-energy coherent spectrum in the background of an incoherent continuum that
extends to higher energies. | cond-mat_dis-nn |
Chain breaking and Kosterlitz-Thouless scaling at the many-body
localization transition in the random field Heisenberg spin chain: Despite tremendous theoretical efforts to understand subtleties of the
many-body localization (MBL) transition, many questions remain open, in
particular concerning its critical properties. Here we make the key observation
that MBL in one dimension is accompanied by a spin freezing mechanism which
causes chain breakings in the thermodynamic limit. Using analytical and
numerical approaches, we show that such chain breakings directly probe the
typical localization length, and that their scaling properties at the MBL
transition agree with the Kosterlitz-Thouless scenario predicted by
phenomenological renormalization group approaches. | cond-mat_dis-nn |
Many-body localization transition in a frustrated XY chain: We demonstrate many-body localization (MBL) transition in a one-dimensional
isotropic XY chain with a weak next-nearest-neighbor frustration in a random
magnetic field. We perform finite-size exact diagonalization calculations of
level-spacing statistics and fractal dimensions to characterize the MBL
transition with increasing the random field amplitude. An equivalent
representation of the model in terms of spinless fermions explains the presence
of the delocalized phase by the appearance of an effective non-local
interaction between the fermions. This interaction appears due to frustration
provided by the next-nearest-neighbor hopping. | cond-mat_dis-nn |
Potts spin glasses with 3, 4 and 5 states near $T=T_c$: expanding around
the replica symmetric solution: Expansion for the free energy functionals of the Potts spin glass models with
3, 4 and 5 states up to the fourth order in $\delta q_{\alpha \beta }$ around
the replica symmetric solution (RS) is investigated using a special
quadrupole-like representation. The temperature dependence of the 1RSB order
parameters is obtained in the vicinity of the point $T=T_c$ where the RS
solution becomes unstable. The crossover from continuous to jumpwise behavior
with increasing of number of states is derived analytically. The comparison is
made of the free energy expansion for the Potts spin glass with that for other
models. | cond-mat_dis-nn |
Clustering of solutions in the symmetric binary perceptron: The geometrical features of the (non-convex) loss landscape of neural network
models are crucial in ensuring successful optimization and, most importantly,
the capability to generalize well. While minimizers' flatness consistently
correlates with good generalization, there has been little rigorous work in
exploring the condition of existence of such minimizers, even in toy models.
Here we consider a simple neural network model, the symmetric perceptron, with
binary weights. Phrasing the learning problem as a constraint satisfaction
problem, the analogous of a flat minimizer becomes a large and dense cluster of
solutions, while the narrowest minimizers are isolated solutions. We perform
the first steps toward the rigorous proof of the existence of a dense cluster
in certain regimes of the parameters, by computing the first and second moment
upper bounds for the existence of pairs of arbitrarily close solutions.
Moreover, we present a non rigorous derivation of the same bounds for sets of
$y$ solutions at fixed pairwise distances. | cond-mat_dis-nn |
Mechanical Failure in Amorphous Solids: Scale Free Spinodal Criticality: The mechanical failure of amorphous media is a ubiquitous phenomenon from
material engineering to geology. It has been noticed for a long time that the
phenomenon is "scale-free", indicating some type of criticality. In spite of
attempts to invoke "Self-Organized Criticality", the physical origin of this
criticality, and also its universal nature, being quite insensitive to the
nature of microscopic interactions, remained elusive. Recently we proposed that
the precise nature of this critical behavior is manifested by a spinodal point
of a thermodynamic phase transition. Moreover, at the spinodal point there
exists a divergent correlation length which is associated with the
system-spanning instabilities (known also as shear bands) which are typical to
the mechanical yield. Demonstrating this requires the introduction of an "order
parameter" that is suitable for distinguishing between disordered amorphous
systems, and an associated correlation function, suitable for picking up the
growing correlation length. The theory, the order parameter, and the
correlation functions used are universal in nature and can be applied to any
amorphous solid that undergoes mechanical yield. Critical exponents for the
correlation length divergence and the system size dependence are estimated. The
phenomenon is seen at its sharpest in athermal systems, as is explained below;
in this paper we extend the discussion also to thermal systems, showing that at
sufficiently high temperatures the spinodal phenomenon is destroyed by thermal
fluctuations. | cond-mat_dis-nn |
Short-time critical dynamics of the three-dimensional systems with
long-range correlated disorder: Monte Carlo simulations of the short-time dynamic behavior are reported for
three-dimensional Ising and XY models with long-range correlated disorder at
criticality, in the case corresponding to linear defects. The static and
dynamic critical exponents are determined for systems starting separately from
ordered and disordered initial states. The obtained values of the exponents are
in a good agreement with results of the field-theoretic description of the
critical behavior of these models in the two-loop approximation and with our
results of Monte Carlo simulations of three-dimensional Ising model in
equilibrium state. | cond-mat_dis-nn |
Odor recognition and segmentation by a model olfactory bulb and cortex: We present a model of an olfactory system that performs odor segmentation.
Based on the anatomy and physiology of natural olfactory systems, it consists
of a pair of coupled modules, bulb and cortex. The bulb encodes the odor inputs
as oscillating patterns. The cortex functions as an associative memory: When
the input from the bulb matches a pattern stored in the connections between its
units, the cortical units resonate in an oscillatory pattern characteristic of
that odor. Further circuitry transforms this oscillatory signal to a
slowly-varying feedback to the bulb. This feedback implements olfactory
segmentation by suppressing the bulbar response to the pre-existing odor,
thereby allowing subsequent odors to be singled out for recognition. | cond-mat_dis-nn |
Neutron Scattering Study of Fluctuating and Static Spin Correlations in
the Anisotropic Spin Glass Fe$_2$TiO$_5$: The anisotropic spin glass transition, in which spin freezing is observed
only along the c-axis in pseudobrookite Fe$_2$TiO$_5$, has long been perplexing
because the Fe$^{3+}$ moments (d$^5$) are expected to be isotropic. Recently,
neutron diffraction demonstrated that surfboard-shaped antiferromagnetic
nanoregions coalesce above the glass transition temperature, T$_g$ $\approx$ 55
K, and a model was proposed in which the freezing of the fluctuations of the
surfboards' magnetization leads to the anisotropic spin glass state. Given this
new model, we have carried out high resolution inelastic neutron scattering
measurements of the spin-spin correlations to understand the temperature
dependence of the intra-surfboard spin dynamics on neutron (picosecond)
time-scales. Here, we report on the temperature-dependence of the spin
fluctuations measured from single crystal Fe$_2$TiO$_5$. Strong quasi-elastic
magnetic scattering, arising from intra-surfboard correlations, is observed
well above T$_g$. The spin fluctuations possess a steep energy-wave vector
relation and are indicative of strong exchange interactions, consistent with
the large Curie-Weiss temperature. As the temperature approaches T$_g$ from
above, a shift in spectral weight from inelastic to elastic scattering is
observed. At various temperatures between 4 K and 300 K, a characteristic
relaxation rate of the fluctuations is determined. Despite the freezing of the
majority of the spin correlations, an inelastic contribution remains even at
base temperature, signifying the presence of fluctuating intra-surfboard spin
correlations to at least T/T$_g$ $\approx$ 0.1 consistent with a description of
Fe$_2$TiO$_5$ as a hybrid between conventional and geometrically frustrated
spin glasses. | cond-mat_dis-nn |
Transverse confinement of ultrasound through the Anderson transition in
3D mesoglasses: We report an in-depth investigation of the Anderson localization transition
for classical waves in three dimensions (3D). Experimentally, we observe clear
signatures of Anderson localization by measuring the transverse confinement of
transmitted ultrasound through slab-shaped mesoglass samples. We compare our
experimental data with predictions of the self-consistent theory of Anderson
localization for an open medium with the same geometry as our samples. This
model describes the transverse confinement of classical waves as a function of
the localization (correlation) length, $\xi$ ($\zeta$), and is fitted to our
experimental data to quantify the transverse spreading/confinement of
ultrasound all of the way through the transition between diffusion and
localization. Hence we are able to precisely identify the location of the
mobility edges at which the Anderson transitions occur. | cond-mat_dis-nn |
Delays, connection topology, and synchronization of coupled chaotic maps: We consider networks of coupled maps where the connections between units
involve time delays. We show that, similar to the undelayed case, the
synchronization of the network depends on the connection topology,
characterized by the spectrum of the graph Laplacian. Consequently, scale-free
and random networks are capable of synchronizing despite the delayed flow of
information, whereas regular networks with nearest-neighbor connections and
their small-world variants generally exhibit poor synchronization. On the other
hand, connection delays can actually be conducive to synchronization, so that
it is possible for the delayed system to synchronize where the undelayed system
does not. Furthermore, the delays determine the synchronized dynamics, leading
to the emergence of a wide range of new collective behavior which the
individual units are incapable of producing in isolation. | cond-mat_dis-nn |
Effect of weak disorder in the Fully Frustrated XY model: The critical behaviour of the Fully Frustrated XY model in presence of weak
positional disorder is studied in a square lattice by Monte Carlo methods. The
critical exponent associated to the divergence of the chiral correlation length
is found to be equal to 1.7 already at very small values of disorder.
Furthermore the helicity modulus jump is found larger than the universal value
expected in the XY model. | cond-mat_dis-nn |
Zero-Temperature Dynamics of Plus/Minus J Spin Glasses and Related
Models: We study zero-temperature, stochastic Ising models sigma(t) on a
d-dimensional cubic lattice with (disordered) nearest-neighbor couplings
independently chosen from a distribution mu on R and an initial spin
configuration chosen uniformly at random. Given d, call mu type I (resp., type
F) if, for every x in the lattice, sigma(x,t) flips infinitely (resp., only
finitely) many times as t goes to infinity (with probability one) --- or else
mixed type M. Models of type I and M exhibit a zero-temperature version of
``local non-equilibration''. For d=1, all types occur and the type of any mu is
easy to determine. The main result of this paper is a proof that for d=2,
plus/minus J models (where each coupling is independently chosen to be +J with
probability alpha and -J with probability 1-alpha) are type M, unlike
homogeneous models (type I) or continuous (finite mean) mu's (type F). We also
prove that all other noncontinuous disordered systems are type M for any d
greater than or equal to 2. The plus/minus J proof is noteworthy in that it is
much less ``local'' than the other (simpler) proof. Homogeneous and plus/minus
J models for d greater than or equal to 3 remain an open problem. | cond-mat_dis-nn |
Extensive eigenvalues in spin-spin correlations: a tool for counting
pure states in Ising spin glasses: We study the nature of the broken ergodicity in the low temperature phase of
Ising spin glass systems, using as a diagnostic tool the spectrum of
eigenvalues of the spin-spin correlation function. We show that multiple
extensive eigenvalues of the correlation matrix $C_{ij}\equiv< S_i S_j>$ occur
if and only if there is replica symmetry breaking. We support our arguments
with Exchange Monte-Carlo results for the infinite-range problem. Here we find
multiple extensive eigenvalues in the RSB phase for $N \agt 200$, but only a
single extensive eigenvalue for phases with long-range order but no RSB.
Numerical results for the short range model in four spatial dimensions, for
$N\le 1296$, are consistent with the presence of a single extensive eigenvalue,
with the subdominant eigenvalue behaving in agreement with expectations derived
from the droplet model. Because of the small system sizes we cannot exclude the
possibility of replica symmetry breaking with finite size corrections in this
regime. | cond-mat_dis-nn |
Entanglement and localization in long-range quadratic Lindbladians: Existence of Anderson localization is considered a manifestation of coherence
of classical and quantum waves in disordered systems. Signatures of
localization have been observed in condensed matter and cold atomic systems
where the coupling to the environment can be significantly suppressed but not
eliminated. In this work we explore the phenomena of localization in random
Lindbladian dynamics describing open quantum systems. We propose a model of
one-dimensional chain of non-interacting, spinless fermions coupled to a local
ensemble of baths. The jump operator mediating the interaction with the bath
linked to each site has a power-law tail with an exponent $p$. We show that the
steady state of the system undergoes a localization entanglement phase
transition by tuning $p$ which remains stable in the presence of coherent
hopping. Unlike the entanglement transition in the quantum trajectories of open
systems, this transition is exhibited by the averaged steady state density
matrix of the Lindbladian. The steady state in the localized phase is
characterised by a heterogeneity in local population imbalance, while the jump
operators exhibit a constant participation ratio of the sites they affect. Our
work provides a novel realisation of localization physics in open quantum
systems. | cond-mat_dis-nn |
Spontaneous ordering against an external field in nonequilibrium systems: We study the collective behavior of nonequilibrium systems subject to an
external field with a dynamics characterized by the existence of
non-interacting states. Aiming at exploring the generality of the results, we
consider two types of models according to the nature of their state variables:
(i) a vector model, where interactions are proportional to the overlap between
the states, and (ii) a scalar model, where interaction depends on the distance
between states. In both cases the system displays three phases: two ordered
phases, one parallel to the field, and another orthogonal to the field; and a
disordered phase. The phase space is numerically characterized for each model
in a fully connected network. By placing the particles on a small-world
network, we show that, while a regular lattice favors the alignment with the
field, the presence of long-range interactions promotes the formation of the
ordered phase orthogonal to the field. | cond-mat_dis-nn |
Unsupervised learning of phase transitions via modified anomaly
detection with autoencoders: In this paper, a modified method of anomaly detection using convolutional
autoencoders is employed to predict phase transitions in several statistical
mechanical models on a square lattice. We show that, when the autoencoder is
trained with input data of various phases, the mean-square-error loss function
can serve as a measure of disorder, and its standard deviation becomes an
excellent indicator of critical points. We find that various types of phase
transition points, including first-order, second-order, and topological ones,
can be faithfully detected by the peaks in the standard deviation of the loss
function. Besides, the values of transition points can be accurately determined
under the analysis of finite-size scaling. Our results demonstrate that the
present approach has general application in identification/classification of
phase transitions even without a priori knowledge of the systems in question. | cond-mat_dis-nn |
Effect of connecting wires on the decoherence due to electron-electron
interaction in a metallic ring: We consider the weak localization in a ring connected to reservoirs through
leads of finite length and submitted to a magnetic field. The effect of
decoherence due to electron-electron interaction on the harmonics of AAS
oscillations is studied, and more specifically the effect of the leads. Two
results are obtained for short and long leads regimes. The scale at which the
crossover occurs is discussed. The long leads regime is shown to be more
realistic experimentally. | cond-mat_dis-nn |
Spin Domains Generate Hierarchical Ground State Structure in J=+/-1 Spin
Glasses: Unbiased samples of ground states were generated for the short-range Ising
spin glass with Jij=+/-1, in three dimensions. Clustering the ground states
revealed their hierarchical structure, which is explained by correlated spin
domains, serving as cores for macroscopic zero energy "excitations". | cond-mat_dis-nn |
Filling a silo with a mixture of grains: Friction-induced segregation: We study the filling process of a two-dimensional silo with inelastic
particles by simulation of a granular media lattice gas (GMLG) model. We
calculate the surface shape and flow profiles for a monodisperse system and we
introduce a novel generalization of the GMLG model for a binary mixture of
particles of different friction properties where, for the first time, we
measure the segregation process on the surface. The results are in good
agreement with a recent theory, and we explain the observed small deviations by
the nonuniform velocity profile. | cond-mat_dis-nn |
Zero-modes in the random hopping model: If the number of lattice sites is odd, a quantum particle hopping on a
bipartite lattice with random hopping between the two sublattices only is
guaranteed to have an eigenstate at zero energy. We show that the localization
length of this eigenstate depends strongly on the boundaries of the lattice,
and can take values anywhere between the mean free path and infinity. The same
dependence on boundary conditions is seen in the conductance of such a lattice
if it is connected to electron reservoirs via narrow leads. For any nonzero
energy, the dependence on boundary conditions is removed for sufficiently large
system sizes. | cond-mat_dis-nn |
Thermodynamic picture of the glassy state gained from exactly solvable
models: A picture for thermodynamics of the glassy state was introduced recently by
us (Phys. Rev. Lett. {\bf 79} (1997) 1317; {\bf 80} (1998) 5580). It starts by
assuming that one extra parameter, the effective temperature, is needed to
describe the glassy state. This approach connects responses of macroscopic
observables to a field change with their temporal fluctuations, and with the
fluctuation-dissipation relation, in a generalized, non-equilibrium way.
Similar universal relations do not hold between energy fluctuations and the
specific heat.
In the present paper the underlying arguments are discussed in greater
length. The main part of the paper involves details of the exact dynamical
solution of two simple models introduced recently: uncoupled harmonic
oscillators subject to parallel Monte Carlo dynamics, and independent spherical
spins in a random field with such dynamics. At low temperature the relaxation
time of both models diverges as an Arrhenius law, which causes glassy behavior
in typical situations. In the glassy regime we are able to verify the above
mentioned relations for the thermodynamics of the glassy state.
In the course of the analysis it is argued that stretched exponential
behavior is not a fundamental property of the glassy state, though it may be
useful for fitting in a limited parameter regime. | cond-mat_dis-nn |
Information Bounds on phase transitions in disordered systems: Information theory, rooted in computer science, and many-body physics, have
traditionally been studied as (almost) independent fields. Only recently has
this paradigm started to shift, with many-body physics being studied and
characterized using tools developed in information theory. In our work, we
introduce a new perspective on this connection, and study phase transitions in
models with randomness, such as localization in disordered systems, or random
quantum circuits with measurements. Utilizing information-based arguments
regarding probability distribution differentiation, we bound critical exponents
in such phase transitions (specifically, those controlling the correlation or
localization lengths). We benchmark our method and rederive the well-known
Harris criterion, bounding critical exponents in the Anderson localization
transition for noninteracting particles, as well as classical disordered spin
systems. We then move on to apply our method to many-body localization. While
in real space our critical exponent bound agrees with recent consensus, we find
that, somewhat surprisingly, numerical results on Fock-space localization for
limited-sized systems do not obey our bounds, indicating that the simulation
results might not hold asymptotically (similarly to what is now believed to
have occurred in the real-space problem). We also apply our approach to random
quantum circuits with random measurements, for which we can derive bounds
transcending recent mappings to percolation problems. | cond-mat_dis-nn |
Impact of boundaries on fully connected random geometric networks: Many complex networks exhibit a percolation transition involving a
macroscopic connected component, with universal features largely independent of
the microscopic model and the macroscopic domain geometry. In contrast, we show
that the transition to full connectivity is strongly influenced by details of
the boundary, but observe an alternative form of universality. Our approach
correctly distinguishes connectivity properties of networks in domains with
equal bulk contributions. It also facilitates system design to promote or avoid
full connectivity for diverse geometries in arbitrary dimension. | cond-mat_dis-nn |
Metallic spin-glasses beyond mean-field: An approach to the
impurity-concentration dependence of the freezing temperature: A relation between the freezing temperature ($T^{}_{\rm g}$) and the exchange
couplings ($J^{}_{ij}$) in metallic spin-glasses is derived, taking the
spin-correlations ($G^{}_{ij}$) into account. This approach does not involve a
disorder-average. The expansion of the correlations to first order in
$J^{}_{ij}/T^{}_{\rm g}$ leads to the molecular-field result from
Thouless-Anderson-Palmer. Employing the current theory of the spin-interaction
in disordered metals, an equation for $T^{}_{\rm g}$ as a function of the
concentration of impurities is obtained, which reproduces the available data
from {\sl Au}Fe, {\sl Ag}Mn, and {\sl Cu}Mn alloys well. | cond-mat_dis-nn |
Finite Temperature Ordering in the Three-Dimensional Gauge Glass: We present results of Monte Carlo simulations of the gauge glass model in
three dimensions using exchange Monte Carlo. We show for the first time clear
evidence of the vortex glass ordered phase at finite temperature. Using finite
size scaling we obtain estimates for the correlation length exponent, nu = 1.39
+/- 0.20, the correlation function exponent, eta = -0.47 +/- 0.07, and the
dynamic exponent z = 4.2 +/- 0.6. Using our values for z and nu we calculate
the resistivity exponent to be s = 4.5 +/- 1.1. Finally, we provide a plausible
lower bound on the the zero-temperature stiffness exponent, theta >= 0.18. | cond-mat_dis-nn |
Saddles and dynamics in a solvable mean-field model: We use the saddle-approach, recently introduced in the numerical
investigation of simple model liquids, in the analysis of a mean-field solvable
system. The investigated system is the k-trigonometric model, a k-body
interaction mean field system, that generalizes the trigonometric model
introduced by Madan and Keyes [J. Chem. Phys. 98, 3342 (1993)] and that has
been recently introduced to investigate the relationship between thermodynamics
and topology of the configuration space. We find a close relationship between
the properties of saddles (stationary points of the potential energy surface)
visited by the system and the dynamics. In particular the temperature
dependence of saddle order follows that of the diffusivity, both having an
Arrhenius behavior at low temperature and a similar shape in the whole
temperature range. Our results confirm the general usefulness of the
saddle-approach in the interpretation of dynamical processes taking place in
interacting systems. | cond-mat_dis-nn |
Random Ising chain in transverse and longitudinal fields: Strong
disorder RG study: Motivated by the compound ${\rm LiHo}_x{\rm Y}_{1-x}{\rm F}_4$, we consider
the Ising chain with random couplings and in the presence of simultaneous
random transverse and longitudinal fields, and study its low-energy properties
at zero temperature by the strong disorder renormalization group approach. In
the absence of longitudinal fields, the system exhibits a quantum-ordered and a
quantum-disordered phase separated by a critical point of infinite disorder.
When the longitudinal random field is switched on, the ordered phase vanishes
and the trajectories of the renormalization group are attracted to two
disordered fixed points: one is characteristic of the classical random field
Ising chain, the other describes the quantum disordered phase. The two
disordered phases are separated by a separatrix that starts at the infinite
disorder fixed point and near which there are strong quantum fluctuations. | cond-mat_dis-nn |
Computing the number of metastable states in infinite-range models: In these notes I will review the results that have been obtained in these
last years on the computation of the number of metastable states in
infinite-range models of disordered systems. This is a particular case of the
problem of computing the exponentially large number of stationary points of a
random function. Quite surprisingly supersymmetry plays a crucial role in this
problem. A careful analysis of the physical implication of supersymmetry and of
supersymmetry breaking will be presented: the most spectacular one is that in
the Sherrington-Kirkpatrick model for spin glasses most of the stationary
points are saddles, as predicted long time ago. | cond-mat_dis-nn |
Dependence of critical parameters of 2D Ising model on lattice size: For the 2D Ising model, we analyzed dependences of thermodynamic
characteristics on number of spins by means of computer simulations. We
compared experimental data obtained using the Fisher-Kasteleyn algorithm on a
square lattice with $N=l{\times}l$ spins and the asymptotic Onsager solution
($N\to\infty$). We derived empirical expressions for critical parameters as
functions of $N$ and generalized the Onsager solution on the case of a
finite-size lattice. Our analytical expressions for the free energy and its
derivatives (the internal energy, the energy dispersion and the heat capacity)
describe accurately the results of computer simulations. We showed that when
$N$ increased the heat capacity in the critical point increased as $lnN$. We
specified restrictions on the accuracy of the critical temperature due to
finite size of our system. Also in the finite-dimensional case, we obtained
expressions describing temperature dependences of the magnetization and the
correlation length. They are in a good qualitative agreement with the results
of computer simulations by means of the dynamic Metropolis Monte Carlo method. | cond-mat_dis-nn |
Experimental Observation of Phase Transitions in Spatial Photonic Ising
Machine: Statistical spin dynamics plays a key role to understand the working
principle for novel optical Ising machines. Here we propose the gauge
transformations for spatial photonic Ising machine, where a single spatial
phase modulator simultaneously encodes spin configurations and programs
interaction strengths. Thanks to gauge transformation, we experimentally
evaluate the phase diagram of high-dimensional spin-glass equilibrium system
with $100$ fully-connected spins. We observe the presence of paramagnetic,
ferromagnetic as well as spin-glass phases and determine the critical
temperature $T_c$ and the critical probability ${{p}_{c}}$ of phase
transitions, which agree well with the mean-field theory predictions. Thus the
approximation of the mean-field model is experimentally validated in the
spatial photonic Ising machine. Furthermore, we discuss the phase transition in
parallel with solving combinatorial optimization problems during the cooling
process and identify that the spatial photonic Ising machine is robust with
sufficient many-spin interactions, even when the system is associated with the
optical aberrations and the measurement uncertainty. | cond-mat_dis-nn |
Ward type identities for the 2d Anderson model at weak disorder: Using the particular momentum conservation laws in dimension d=2, we can
rewrite the Anderson model in terms of low momentum long range fields, at the
price of introducing electron loops. The corresponding loops satisfy a Ward
type identity, hence are much smaller than expected. This fact should be useful
for a study of the weak-coupling model in the middle of the spectrum of the
free Hamiltonian. | cond-mat_dis-nn |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.