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Neural networks and logical reasoning systems. A translation table: A correspondence is established between the elements of logic reasoning
systems (knowledge bases, rules, inference and queries) and the hardware and
dynamical operations of neural networks. The correspondence is framed as a
general translation dictionary which, hopefully, will allow to go back and
forth between symbolic and network formulations, a desirable step in
learning-oriented systems and multicomputer networks. In the framework of Horn
clause logics it is found that atomic propositions with n arguments correspond
to nodes with n-th order synapses, rules to synaptic intensity constraints,
forward chaining to synaptic dynamics and queries either to simple node
activation or to a query tensor dynamics. | cond-mat_dis-nn |
Disorder-Induced Vibrational Localization: The vibrational equivalent of the Anderson tight-binding Hamiltonian has been
studied, with particular focus on the properties of the eigenstates at the
transition from extended to localized states. The critical energy has been
found approximately for several degrees of force-constant disorder using
system-size scaling of the multifractal spectra of the eigenmodes, and the
spectrum at which there is no system-size dependence has been obtained. This is
shown to be in good agreement with the critical spectrum for the electronic
problem, which has been derived both numerically and by analytic means.
Universality of the critical states is therefore suggested also to hold for the
vibrational problem. | cond-mat_dis-nn |
Energy statistics in disordered systems: The local REM conjecture and
beyond: Recently, Bauke and Mertens conjectured that the local statistics of energies
in random spin systems with discrete spin space should in most circumstances be
the same as in the random energy model. Here we give necessary conditions for
this hypothesis to be true, which we show to hold in wide classes of examples:
short range spin glasses and mean field spin glasses of the SK type. We also
show that, under certain conditions, the conjecture holds even if energy levels
that grow moderately with the volume of the system are considered. In the case
of the Generalised Random energy model, we give a complete analysis for the
behaviour of the local energy statistics at all energy scales. In particular,
we show that, in this case, the REM conjecture holds exactly up to energies
$E_N<\b_c N$, where $\b_c$ is the critical temperature. We also explain the
more complex behaviour that sets in at higher energies. | cond-mat_dis-nn |
Two Interacting Electrons in a Quasiperiodic Chain: We study numerically the effect of on-site Hubbard interaction U between two
electrons in the quasiperiodic Harper's equation. In the periodic chain limit
by mapping the problem to that of one electron in two dimensions with a
diagonal line of impurities of strength U we demonstrate a band of resonance
two particle pairing states starting from E=U. In the ballistic (metallic)
regime we show explicitly interaction-assisted extended pairing states and
multifractal pairing states in the diffusive (critical) regime. We also obtain
localized pairing states in the gaps and the created subband due to U, whose
number increases when going to the localized regime, which are responsible for
reducing the velocity and the diffusion coefficient in the qualitatively
similar to the non-interacting case ballistic and diffusive dynamics. In the
localized regime we find propagation enhancement for small U and stronger
localization for larger U, as in disordered systems. | cond-mat_dis-nn |
Significance of the Hyperfine Interactions in the Phase Diagram of ${\rm
LiHo_xY_{1-x}F_4}$: We consider the quantum magnet $\rm LiHo_xY_{1-x}F_4$ at $x = 0.167$.
Experimentally the spin glass to paramagnet transition in this system was
studied as a function of the transverse magnetic field and temperature, showing
peculiar features: for example (i) the spin glass order is destroyed much
faster by thermal fluctuations than by the transverse field; and (ii) the cusp
in the nonlinear susceptibility signaling the glass state {\it decreases} in
size at lower temperature. Here we show that the hyperfine interactions of the
Ho atom must dominate in this system, and that along with the transverse
inter-Ho dipolar interactions they dictate the structure of the phase diagram.
The experimental observations are shown to be natural consequences of this. | cond-mat_dis-nn |
Resilience to damage of graphs with degree correlations: The existence or not of a percolation threshold on power law correlated
graphs is a fundamental question for which a general criterion is lacking. In
this work we investigate the problems of site and bond percolation on graphs
with degree correlations and their connection with spreading phenomena. We
obtain some general expressions that allow the computation of the transition
thresholds or their bounds. Using these results we study the effects of
assortative and disassortative correlations on the resilience to damage of
networks. | cond-mat_dis-nn |
Effect of second-rank random anisotropy on critical phenomena of random
field O(N) spin model in the large N limit: We study the critical behavior of a random field O($N$) spin model with a
second-rank random anisotropy term in spatial dimensions $4<d<6$, by means of
the replica method and the 1/N expansion. We obtain a replica-symmetric
solution of the saddle-point equation, and we find the phase transition obeying
dimensional reduction. We study the stability of the replica-symmetric saddle
point against the fluctuation induced by the second-rank random anisotropy. We
show that the eigenvalue of the Hessian at the replica-symmetric saddle point
is strictly positive. Therefore, this saddle point is stable and the
dimensional reduction holds in the 1/N expansion. To check the consistency with
the functional renormalization group method, we obtain all fixed points of the
renormalization group in the large $N$ limit and discuss their stability. We
find that the analytic fixed point yielding the dimensional reduction is
practically singly unstable in a coupling constant space of the given model
with large $N$. Thus, we conclude that the dimensional reduction holds for
sufficiently large $N$. | cond-mat_dis-nn |
Are Bosonic Replicas Faulty?: Motivated by the ongoing discussion about a seeming asymmetry in the
performance of fermionic and bosonic replicas, we present an exact,
nonperturbative approach to zero-dimensional replica field theories belonging
to the broadly interpreted "beta=2" Dyson symmetry class. We then utilise the
formalism developed to demonstrate that the bosonic replicas do correctly
reproduce the microscopic spectral density in the QCD inspired chiral Gaussian
unitary ensemble. This disproves the myth that the bosonic replica field
theories are intrinsically faulty. | cond-mat_dis-nn |
Linearized spectral decimation in fractals: In this article we study the energy level spectrum of fractals which have
block-hierarchical structures. We develop a method to study the spectral
properties in terms of linearization of spectral decimation procedure and
verify it numerically. Our approach provides qualitative explanations for
various spectral properties of self-similar graphs within the theory of
dynamical systems, including power-law level-spacing distribution, smooth
density of states and effective chaotic regime. | cond-mat_dis-nn |
Disorder driven phase transitions in weak AIII topological insulators: The tenfold classification of topological phases enumerates all strong
topological phases for both clean and disordered systems. These strong
topological phases are connected to the existence of robust edge states.
However, in addition to the strong topological phases in the tenfold
classification, there exist weak topological phases whose properties under
disorder are less well understood. It is unknown if the weak topological
indices can be generalized for arbitrary disorder, and the physical signatures
of these indices is not known. In this paper, we study disordered models of the
two dimensional weak AIII insulator. We demonstrate that the weak invariants
can be defined at arbitrary disorder, and that these invariants are connected
to the presence or absence of bound charge at dislocation sites. | cond-mat_dis-nn |
Chemical order lifetimes in liquids in the energy landscape paradigm: Recent efforts to deal with the complexities of the liquid state,
particularly those of glassforming systems, have focused on the "energy
landscape" as a means of dealing with the collective variables problem [1]. The
"basins of attraction" that constitute the landscape features in configuration
space represent a distinct class of microstates of the system. So far only the
microstates that are related to structural relaxation and viscosity have been
considered in this paradigm. But most of the complex systems of importance in
nature and industry are solutions, particularly solutions that are highly
non-ideal in character. In these, a distinct class of fluctuations exists, the
fluctuations in concentration. The mean square amplitudes of these fluctuations
relate to the chemical activity coefficients [2], and their rise and decay
times may be much longer than those of the density fluctuations - from which
they may be statistically independent. Here we provide data on the character of
chemical order fluctuations in viscous liquids and on their relation to the
enthalpy fluctuations that determine the structural relaxation time, and hence
the glass temperature Tg. Using a spectroscopically active chemical order
probe, we identify a "chemical fictive temperature", Tchm, by analogy with the
familiar "fictive temperature" Tf (the cooling Tg). Like Tf, Tchm must be the
same as the real temperature for the system to be in complete equilibrium. It
is possible for mobile multicomponent liquids to be permanently nonergodic,
insofar as Tchm > Tf = T, which must be accommodated within the landscape
paradigm. We note that, in appropriate systems, an increase in concentration of
slow chemically ordering units in liquids can produce a crossover to fast ion
conducting glass phenomenology. | cond-mat_dis-nn |
Molecular dynamics computer simulation of amorphous silica under high
pressure: The structural and dynamic properties of silica melts under high pressure are
studied using molecular dynamics (MD) computer simulation. The interactions
between the ions are modeled by a pairwise-additive potential, the so-called
CHIK potential, that has been recently proposed by Carre et al. The
experimental equation of state is well-reproduced by the CHIK model. With
increasing pressure (density), the structure changes from a tetrahedral network
to a network containing a high number of five- and six-fold Si-O coordination.
In the partial static structure factors, this change of the structure with
increasing density is reflected by a shift of the first sharp diffraction peak
towards higher wavenumbers q, eventually merging with the main peak at
densities around 4.2 g/cm^3. The self-diffusion constants as a function of
pressure show the experimentally-known maximum, occurring around a pressure of
about 20 GPa. | cond-mat_dis-nn |
Renormalization Group Approach to Spin Glass Systems: A renormalization group transformation suitable for spin glass models and,
more generally, for disordered models, is presented. The procedure is
non-standard in both the nature of the additional interactions and the coarse
graining transformation, that is performed on the overlap probability measure
(which is clearly non-Gibbsian). Universality classes are thus naturally
defined on a large set of models, going from $\Z_2$ and Gaussian spin glasses
to Ising and fully frustrated models, and others. | cond-mat_dis-nn |
Mobility edge and intermediate phase in one-dimensional incommensurate
lattice potentials: We study theoretically the localization properties of two distinct
one-dimensional quasiperiodic lattice models with a single-particle mobility
edge (SPME) separating extended and localized states in the energy spectrum.
The first one is the familiar Soukoulis-Economou trichromatic potential model
with two incommensurate potentials, and the second is a system consisting of
two coupled 1D Aubry-Andre chains each containing one incommensurate potential.
We show that as a function of the Hamiltonian model parameters, both models
have a wide single-particle intermediate phase (SPIP), defined as the regime
where localized and extended single-particle states coexist in the spectrum,
leading to a behavior intermediate between purely extended or purely localized
when the system is dynamically quenched from a generic initial state. Our
results thus suggest that both systems could serve as interesting experimental
platforms for studying the interplay between localized and extended states, and
may provide insight into the role of the coupling of small baths to localized
systems. We also calculate the Lyapunov (or localization) exponent for several
incommensurate 1D models exhibiting SPME, finding that such localization
critical exponents for quasiperiodic potential induced localization are
nonuniversal and depend on the microscopic details of the Hamiltonian. | 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 |
k-Core percolation on multiplex networks: We generalize the theory of k-core percolation on complex networks to k-core
percolation on multiplex networks, where k=(k_a, k_b, ...). Multiplex networks
can be defined as networks with a set of vertices but different types of edges,
a, b, ..., representing different types of interactions. For such networks, the
k-core is defined as the largest sub-graph in which each vertex has at least
k_i edges of each type, i = a, b, ... . We derive self-consistency equations to
obtain the birth points of the k-cores and their relative sizes for
uncorrelated multiplex networks with an arbitrary degree distribution. To
clarify our general results, we consider in detail multiplex networks with
edges of two types, a and b, and solve the equations in the particular case of
ER and scale-free multiplex networks. We find hybrid phase transitions at the
emergence points of k-cores except the (1,1)-core for which the transition is
continuous. We apply the k-core decomposition algorithm to air-transportation
multiplex networks, composed of two layers, and obtain the size of (k_a,
k_b)-cores. | cond-mat_dis-nn |
Comment on "Collective dynamics in liquid lithium, sodium, and aluminum": In a recent paper, S. Singh and K. Tankeshwar (ST), [Phys. Rev. E
\textbf{67}, 012201 (2003)], proposed a new interpretation of the collective
dynamics in liquid metals, and, in particular, of the relaxation mechanisms
ruling the density fluctuations propagation. At variance with both the
predictions of the current literature and the results of recent Inelastic X-ray
Scattering (IXS) experiments, ST associate the quasielastic component of the
$S(Q,\omega)$ to the thermal relaxation, as it holds in an ordinary adiabatic
hydrodynamics valid for non-conductive liquids and in the $Q \to 0$ limit. We
show here that this interpretation leads to a non-physical behaviour of
different thermodynamic and transport parameters. | cond-mat_dis-nn |
Breakdown of Dynamical Scale Invariance in the Coarsening of Fractal
Clusters: We extend a previous analysis [PRL {\bf 80}, 4693 (1998)] of breakdown of
dynamical scale invariance in the coarsening of two-dimensional DLAs
(diffusion-limited aggregates) as described by the Cahn-Hilliard equation.
Existence of a second dynamical length scale, predicted earlier, is
established. Having measured the "solute mass" outside the cluster versus time,
we obtain a third dynamical exponent. An auxiliary problem of the dynamics of a
slender bar (that acquires a dumbbell shape) is considered. A simple scenario
of coarsening of fractal clusters with branching structure is suggested that
employs the dumbbell dynamics results. This scenario involves two dynamical
length scales: the characteristic width and length of the cluster branches. The
predicted dynamical exponents depend on the (presumably invariant) fractal
dimension of the cluster skeleton. In addition, a robust theoretical estimate
for the third dynamical exponent is obtained. Exponents found numerically are
in reasonable agreement with these predictions. | cond-mat_dis-nn |
Exact new mobility edges between critical and localized states: The disorder systems host three types of fundamental quantum states, known as
the extended, localized, and critical states, of which the critical states
remain being much less explored. Here we propose a class of exactly solvable
models which host a novel type of exact mobility edges (MEs) separating
localized states from robust critical states, and propose experimental
realization. Here the robustness refers to the stability against both
single-particle perturbation and interactions in the few-body regime. The
exactly solvable one-dimensional models are featured by quasiperiodic mosaic
type of both hopping terms and on-site potentials. The analytic results enable
us to unambiguously obtain the critical states which otherwise require arduous
numerical verification including the careful finite size scalings. The critical
states and new MEs are shown to be robust, illustrating a generic mechanism
unveiled here that the critical states are protected by zeros of quasiperiodic
hopping terms in the thermodynamic limit. Further, we propose a novel
experimental scheme to realize the exactly solvable model and the new MEs in an
incommensurate Rydberg Raman superarray. This work may pave a way to precisely
explore the critical states and new ME physics with experimental feasibility. | cond-mat_dis-nn |
Critical exponents in Ising spin glasses: We determine accurate values of ordering temperatures and critical exponents
for Ising Spin Glass transitions in dimension 4, using a combination of finite
size scaling and non-equilibrium scaling techniques. We find that the exponents
$\eta$ and $z$ vary with the form of the interaction distribution, indicating
non-universality at Ising spin glass transitions. These results confirm
conclusions drawn from numerical data for dimension 3. | cond-mat_dis-nn |
On the fragility of the mean-field scenario of structural glasses for
finite-dimensional disordered spin models: At the mean-field level, on fully connected lattices, several disordered spin
models have been shown to belong to the universality class of "structural
glasses", with a "random first-order transition" (RFOT) characterized by a
discontinuous jump of the order parameter and no latent heat. However, their
behavior in finite dimensions is often drastically different, displaying either
no glassiness at all or a conventional spin-glass transition. We clarify the
physical reasons for this phenomenon and stress the unusual fragility of the
RFOT to short-range fluctuations, associated e.g. with the mere existence of a
finite number of neighbors. Accordingly, the solution of fully connected models
is only predictive in very high dimension whereas, despite being also
mean-field in character, the Bethe approximation provides valuable information
on the behavior of finite-dimensional systems. We suggest that before embarking
on a full-blown account of fluctuations on all scales through computer
simulation or renormalization-group approach, models for structural glasses
should first be tested for the effect of short-range fluctuations and we
discuss ways to do it. Our results indicate that disordered spin models do not
appear to pass the test and are therefore questionable models for investigating
the glass transition in three dimensions. This also highlights how nontrivial
is the first step of deriving an effective theory for the RFOT phenomenology
from a rigorous integration over the short-range fluctuations. | cond-mat_dis-nn |
Circumventing spin glass traps by microcanonical spontaneous symmetry
breaking: The planted p-spin interaction model is a paradigm of random-graph systems
possessing both a ferromagnetic phase and a disordered phase with the latter
splitting into many spin glass states at low temperatures. Conventional
simulated annealing dynamics is easily blocked by these low-energy spin glass
states. Here we demonstrate that, actually this planted system is exponentially
dominated by a microcanonical polarized phase at intermediate energy densities.
There is a discontinuous microcanonical spontaneous symmetry breaking
transition from the paramagnetic phase to the microcanonical polarized phase.
This transition can serve as a mechanism to avoid all the spin glass traps, and
it is accelerated by the restart strategy of microcanonical random walk. We
also propose an unsupervised learning problem on microcanonically sampled
configurations for inferring the planted ground state. | cond-mat_dis-nn |
Dynamics of fractal dimension during phase ordering of a geometrical
multifractal: A simple multifractal coarsening model is suggested that can explain the
observed dynamical behavior of the fractal dimension in a wide range of
coarsening fractal systems. It is assumed that the minority phase (an ensemble
of droplets) at $t=0$ represents a non-uniform recursive fractal set, and that
this set is a geometrical multifractal characterized by a $f(\alpha)$-curve. It
is assumed that the droplets shrink according to their size and preserving
their ordering. It is shown that at early times the Hausdorff dimension does
not change with time, whereas at late times its dynamics follow the $f(\alpha)$
curve. This is illustrated by a special case of a two-scale Cantor dust. The
results are then generalized to a wider range of coarsening mechanisms. | cond-mat_dis-nn |
Atomic structure of the continuous random network of amorphous
C[(C6H4)2]2, PAF-1: We demonstrate that the amorphous material PAF-1, C[(C6H4)2]2, forms a
continuous random network in which tetrahedral carbon sites are connected by
4,4'-biphenyl linkers. Experimental neutron total scattering measurements on
deuterated, hydrogenous, and null-scattering samples agree with molecular
dynamics simulations based on this model. From the MD model, we are able for
the first time to interrogate the atomistic structure. The small-angle
scattering is consistent with Porod scattering from particle surfaces, of the
form Q^{-4}, where Q is the scattering vector. We measure a distinct peak in
the scattering at Q = 0.45 {\AA}^{-1}, corresponding to the first sharp
diffraction peak in amorphous silica, which indicates the structural analogy
between these two amorphous tetrahedral networks. | cond-mat_dis-nn |
Finite size effects in the microscopic critical properties of jammed
configurations: A comprehensive study of the effects of different types of
disorder: Jamming criticality defines a universality class that includes systems as
diverse as glasses, colloids, foams, amorphous solids, constraint satisfaction
problems, neural networks, etc. A particularly interesting feature of this
class is that small interparticle forces ($f$) and gaps ($h$) are distributed
according to nontrivial power laws. A recently developed mean-field (MF) theory
predicts the characteristic exponents of these distributions in the limit of
very high spatial dimension, $d\rightarrow\infty$ and, remarkably, their values
seemingly agree with numerical estimates in physically relevant dimensions,
$d=2$ and $3$. These exponents are further connected through a pair of
inequalities derived from stability conditions, and both theoretical
predictions and previous numerical investigations suggest that these
inequalities are saturated. Systems at the jamming point are thus only
marginally stable. Despite the key physical role played by these exponents,
their systematic evaluation has yet to be attempted. Here, we carefully test
their value by analyzing the finite-size scaling of the distributions of $f$
and $h$ for various particle-based models for jamming. Both dimension and the
direction of approach to the jamming point are also considered. We show that,
in all models, finite-size effects are much more pronounced in the distribution
of $h$ than in that of $f$. We thus conclude that gaps are correlated over
considerably longer scales than forces. Additionally, remarkable agreement with
MF predictions is obtained in all but one model, namely near-crystalline
packings. Our results thus help to better delineate the domain of the jamming
universality class. We furthermore uncover a secondary linear regime in the
distribution tails of both $f$ and $h$. This surprisingly robust feature is
understood to follow from the (near) isostaticity of our configurations. | cond-mat_dis-nn |
Rayleigh anomalies and disorder-induced mixing of polarizations at
nanoscale in amorphous solids. Testing 1-octyl-3-methylimidazolium chloride
glass: Acoustic excitations in topologically disordered media at mesoscale present
anomalous features with respect to the Debye's theory. In a three-dimensional
medium an acoustic excitation is characterized by its phase velocity, intensity
and polarization. The so-called Rayleigh anomalies, which manifest in
attenuation and retardation of the acoustic excitations, affect the first two
properties. The topological disorder is, however, expected to influence also
the third one. Acoustic excitations with a well-defined polarization in the
continuum limit present indeed a so-called mixing of polarizations at
nanoscale, as attested by experimental observations and Molecular Dynamics
simulations. We provide a comprehensive experimental characterization of
acoustic dynamics properties of a selected glass, 1-octyl-3-methylimidazolium
chloride glass, whose heterogeneous structure at nanoscale is well-assessed.
Distinctive features, which can be related to the occurrence of the Rayleigh
anomalies and of the mixing of polarizations are observed. We develop, in the
framework of the Random Media Theory, an analytical model that allows a
quantitative description of all the Rayleigh anomalies and the mixing of
polarizations. Contrast between theoretical and experimental features for the
selected glass reveals an excellent agreement. The quantitative theoretical
approach permits thus to demonstrate how the mixing of polarizations generates
distinctive feature in the dynamic structure factor of glasses and to
unambiguously identify them. The robustness of the proposed theoretical
approach is validated by its ability to describe as well transverse acoustic
dynamics. | cond-mat_dis-nn |
Mott, Floquet, and the response of periodically driven Anderson
insulators: We consider periodically driven Anderson insulators. The short time behavior
for weak, monochromatic, uniform electric fields is given by linear response
theory and was famously derived by Mott. We go beyond this to consider both
long times---which is the physics of Floquet late time states---and strong
electric fields. This results in a `phase diagram' in the frequency-field
strength plane, in which we identify four distinct regimes. These are: a linear
response regime dominated by pre-existing Mott resonances, which exists
provided Floquet saturation is not reached within a period; a non-linear
perturbative regime, which exhibits multiphoton-absorption in response to the
field; a near-adiabatic regime, which exhibits a primarily reactive response
spread over the entire sample and is insensitive to pre-existing resonances;
and finally an enhanced dissipative regime. | cond-mat_dis-nn |
Phase Transition in a Random Minima Model: Mean Field Theory and Exact
Solution on the Bethe Lattice: We consider the number and distribution of minima in random landscapes
defined on non-Euclidean lattices. Using an ensemble where random landscapes
are reweighted by a fugacity factor $z$ for each minimum they contain, we
construct first a `two-box' mean field theory. This exhibits an ordering phase
transition at $z\c=2$ above which one box contains an extensive number of
minima. The onset of order is governed by an unusual order parameter exponent
$\beta=1$, motivating us to study the same model on the Bethe lattice. Here we
find from an exact solution that for any connectivity $\mu+1>2$ there is an
ordering transition with a conventional mean field order parameter exponent
$\beta=1/2$, but with the region where this behaviour is observable shrinking
in size as $1/\mu$ in the mean field limit of large $\mu$. We show that the
behaviour in the transition region can also be understood directly within a
mean field approach, by making the assignment of minima `soft'. Finally we
demonstrate, in the simplest mean field case, how the analysis can be
generalized to include both maxima and minima. In this case an additional first
order phase transition appears, to a landscape in which essentially all sites
are either minima or maxima. | cond-mat_dis-nn |
Logarithmically Slow Relaxation in Quasi-Periodically Driven Random Spin
Chains: We simulate the dynamics of a disordered interacting spin chain subject to a
quasi-periodic time-dependent drive, corresponding to a stroboscopic Fibonacci
sequence of two distinct Hamiltonians. Exploiting the recursive drive
structure, we can efficiently simulate exponentially long times. After an
initial transient, the system exhibits a long-lived glassy regime characterized
by a logarithmically slow growth of entanglement and decay of correlations
analogous to the dynamics at the many-body delocalization transition.
Ultimately, at long time-scales, which diverge exponentially for weak or rapid
drives, the system thermalizes to infinite temperature. The slow relaxation
enables metastable dynamical phases, exemplified by a "time quasi-crystal" in
which spins exhibit persistent oscillations with a distinct quasi-periodic
pattern from that of the drive. We show that in contrast with Floquet systems,
a high-frequency expansion strictly breaks down above fourth order, and fails
to produce an effective static Hamiltonian that would capture the pre-thermal
glassy relaxation. | cond-mat_dis-nn |
Comment on "Explicit Analytical Solution for Random Close Packing in d=2
and d=3", Physical Review Letters {\bf 128}, 028002 (2022): The method, proposed in \cite{Za22} to derive the densest packing fraction of
random disc and sphere packings, is shown to yield in two dimensions too high a
value that (i) violates the very assumption underlying the method and (ii)
corresponds to a high degree of structural order. The claim that the obtained
value is supported by a specific simulation is shown to be unfounded. One
source of the error is pointed out. | cond-mat_dis-nn |
Fluctuations in photon local delay time and their relation to phase
spectra in random media: The temporal evolution of microwave pulses transmitted through random
dielectric samples is obtained from the Fourier transform of field spectra.
Large fluctuations are found in the local or single channel delay time, which
is the first temporal moment of the transmitted pulse at a point in the output
speckle pattern. Both positive and negative values of local delay time are
observed. The widest distribution is found at low intensity values near a phase
singularity in the transmitted speckle pattern. In the limit of long duration,
narrow-bandwidth incident pulses, the single channel delay time equals the
spectral derivative of the phase of the transmitted field. Fluctuations of the
phase of the transmitted field thus reflect the underlying statistics of
dynamics in mesoscopic systems. | cond-mat_dis-nn |
Order Parameter Criticality of the d=3 Random-Field Ising
Antiferromagnet Fe(0.85)Zn(0.15)F2: The critical exponent beta =0.16 +- 0.02 for the random-field Ising model
order parameter is determined using extinction-free magnetic x-ray scattering
for Fe(0.85)Zn(0.15)F2 in magnetic fields of 10 and 11 T. The observed value is
consistent with other experimental random-field critical exponents, but
disagrees sharply with Monte Carlo and exact ground state calculations on
finite-sized systems. | cond-mat_dis-nn |
Non-perturbative results for level correlations from the replica
nonlinear sigma model: We show that for all the three standard symmetry classes (unitary, orthogonal
and symplectic), the conventional replica nonlinear sigma model gives the
correct non-perturbative result for the two-level correlation functions
R_2(\omega) of electrons in disordered metals in the limit of large \omega. In
this limit, non-perturbative oscillatory contributions arise from a degenerate
saddle-point manifold within this sigma model which corresponds to the
replica-symmetry breaking. Moreover, we demonstrate that in the unitary case
the very same results can be extracted from the well known exact integral
representation for R_2(\omega). | cond-mat_dis-nn |
Phase transitions in the $q$-coloring of random hypergraphs: We study in this paper the structure of solutions in the random hypergraph
coloring problem and the phase transitions they undergo when the density of
constraints is varied. Hypergraph coloring is a constraint satisfaction problem
where each constraint includes $K$ variables that must be assigned one out of
$q$ colors in such a way that there are no monochromatic constraints, i.e.
there are at least two distinct colors in the set of variables belonging to
every constraint. This problem generalizes naturally coloring of random graphs
($K=2$) and bicoloring of random hypergraphs ($q=2$), both of which were
extensively studied in past works. The study of random hypergraph coloring
gives us access to a case where both the size $q$ of the domain of the
variables and the arity $K$ of the constraints can be varied at will. Our work
provides explicit values and predictions for a number of phase transitions that
were discovered in other constraint satisfaction problems but never evaluated
before in hypergraph coloring. Among other cases we revisit the hypergraph
bicoloring problem ($q=2$) where we find that for $K=3$ and $K=4$ the
colorability threshold is not given by the one-step-replica-symmetry-breaking
analysis as the latter is unstable towards more levels of replica symmetry
breaking. We also unveil and discuss the coexistence of two different 1RSB
solutions in the case of $q=2$, $K \ge 4$. Finally we present asymptotic
expansions for the density of constraints at which various phase transitions
occur, in the limit where $q$ and/or $K$ diverge. | cond-mat_dis-nn |
Dynamic mean-field and cavity methods for diluted Ising systems: We compare dynamic mean-field and dynamic cavity as methods to describe the
stationary states of dilute kinetic Ising models. We compute dynamic mean-field
theory by expanding in interaction strength to third order, and compare to the
exact dynamic mean-field theory for fully asymmetric networks. We show that in
diluted networks the dynamic cavity method generally predicts magnetizations of
individual spins better than both first order ("naive") and second order
("TAP") dynamic mean field theory. | cond-mat_dis-nn |
Breakdown of self-averaging in the Bose glass: We study the square-lattice Bose-Hubbard model with bounded random on-site
energies at zero temperature. Starting from a dual representation obtained from
a strong-coupling expansion around the atomic limit, we employ a real-space
block decimation scheme. This approach is non-perturbative in the disorder and
enables us to study the renormalization-group flow of the induced random-mass
distribution. In both insulating phases, the Mott insulator and the Bose glass,
the average mass diverges, signaling short range superfluid correlations. The
relative variance of the mass distribution distinguishes the two phases,
renormalizing to zero in the Mott insulator and diverging in the Bose glass.
Negative mass values in the tail of the distribution indicate the presence of
rare superfluid regions in the Bose glass. The breakdown of self-averaging is
evidenced by the divergent relative variance and increasingly non-Gaussian
distributions. We determine an explicit phase boundary between the Mott
insulator and Bose glass. | cond-mat_dis-nn |
Dynamics of quantum information in many-body localized systems: We characterize the information dynamics of strongly disordered systems using
a combination of analytics, exact diagonalization, and matrix product operator
simulations. More specifically, we study the spreading of quantum information
in three different scenarios: thermalizing, Anderson localized, and many-body
localized. We qualitatively distinguish these cases by quantifying the amount
of remnant information in a local region. The nature of the dynamics is further
explored by computing the propagation of mutual information with respect to
varying partitions. Finally, we demonstrate that classical simulability, as
captured by the magnitude of MPO truncation errors, exhibits enhanced
fluctuations near the localization transition, suggesting the possibility of
its use as a diagnostic of the critical point. | cond-mat_dis-nn |
Comment on "Collective dynamics in liquid lithium, sodium, and aluminum": In a recent paper, S. Singh and K. Tankeshwar (ST), [Phys. Rev. E
\textbf{67}, 012201 (2003)], proposed a new interpretation of the collective
dynamics in liquid metals, and, in particular, of the relaxation mechanisms
ruling the density fluctuations propagation. At variance with both the
predictions of the current literature and the results of recent Inelastic X-ray
Scattering (IXS) experiments, ST associate the quasielastic component of the
$S(Q,\omega)$ to the thermal relaxation, as it holds in an ordinary adiabatic
hydrodynamics valid for non-conductive liquids and in the $Q \to 0$ limit. We
show here that this interpretation leads to a non-physical behaviour of
different thermodynamic and transport parameters. | cond-mat_dis-nn |
Many-body localization as a large family of localized ground states: Many-body localization (MBL) addresses the absence of thermalization in
interacting quantum systems, with non-ergodic high-energy eigenstates behaving
as ground states, only area-law entangled. However, computing highly excited
many-body eigenstates using exact methods is very challenging. Instead, we show
that one can address high-energy MBL physics using ground-state methods, which
are much more amenable to many efficient algorithms. We find that a localized
many-body ground state of a given interacting disordered Hamiltonian
$\mathcal{H}_0$ is a very good approximation for a high-energy eigenstate of a
parent Hamiltonian, close to $\mathcal{H}_0$ but more disordered. This
construction relies on computing the covariance matrix, easily achieved using
density-matrix renormalization group for disordered Heisenberg chains up to
$L=256$ sites. | cond-mat_dis-nn |
Exact results and new insights for models defined over small-world
networks. First and second order phase transitions. I: General result: We present, as a very general method, an effective field theory to analyze
models defined over small-world networks. Even if the exactness of the method
is limited to the paramagnetic regions and to some special limits, it gives the
exact critical behavior and the exact critical surfaces and percolation
thresholds, and provide a clear and immediate (also in terms of calculation)
insight of the physics. The underlying structure of the non random part of the
model, i.e., the set of spins staying in a given lattice L_0 of dimension d_0
and interacting through a fixed coupling J_0, is exactly taken into account.
When J_0\geq 0, the small-world effect gives rise to the known fact that a
second order phase transition takes place, independently of the dimension d_0
and of the added random connectivity c. However, when J_0<0, a completely
different scenario emerges where, besides a spin glass transition, multiple
first- and second-order phase transitions may take place. | cond-mat_dis-nn |
Lack of Evidence for a Singlet Crystal Field Ground State in the
Tb2Ti2O7 Magnetic Pyrochlore: We present new high resolution inelastic neutron scattering data on the
candidate spin liquid Tb2Ti2O7. We find that there is no evidence for a zero
field splitting of the ground state doublet within the 0.2 K resolution of the
instrument. This result contrasts with a pair of recent works on Tb2Ti2O7
claiming that the spin liquid behavior can be attributed to a 2 K split
singlet-singlet single-ion spectrum at low energies. We also reconsider the
entropy argument presented in Chapuis {\it et al.} as further evidence of a
singlet-singlet crystal field spectrum. We arrive at the conclusion that
estimates of the low temperature residual entropy drawn from heat capacity
measurements are a poor guide to the single ion spectrum without understanding
the nature of the correlations. | cond-mat_dis-nn |
Jamming and replica symmetry breaking of weakly disordered crystals: We discuss the physics of crystals with small polydispersity near the jamming
transition point. For this purpose, we introduce an effective single-particle
model taking into account the nearest neighbor structure of crystals. The model
can be solved analytically by using the replica method in the limit of large
dimensions. In the absence of polydispersity, the replica symmetric solution is
stable until the jamming transition point, which leads to the standard scaling
of perfect crystals. On the contrary, for finite polydispersity, the model
undergoes the full replica symmetry breaking (RSB) transition before the
jamming transition point. In the RSB phase, the model exhibits the same scaling
as amorphous solids near the jamming transition point. These results are fully
consistent with the recent numerical simulations of crystals with
polydispersity. The simplicity of the model also allows us to derive the
scaling behavior of the vibrational density of states that can be tested in
future experiments and numerical simulations. | cond-mat_dis-nn |
Universal scaling of distances in complex networks: Universal scaling of distances between vertices of Erdos-Renyi random graphs,
scale-free Barabasi-Albert models, science collaboration networks, biological
networks, Internet Autonomous Systems and public transport networks are
observed. A mean distance between two nodes of degrees k_i and k_j equals to
<l_{ij}>=A-B log(k_i k_j). The scaling is valid over several decades. A simple
theory for the appearance of this scaling is presented. Parameters A and B
depend on the mean value of a node degree <k>_nn calculated for the nearest
neighbors and on network clustering coefficients. | cond-mat_dis-nn |
Application of a multi-site mean-field theory to the disordered
Bose-Hubbard model: We present a multi-site formulation of mean-field theory applied to the
disordered Bose-Hubbard model. In this approach the lattice is partitioned into
clusters, each isolated cluster being treated exactly, with inter-cluster
hopping being treated approximately. The theory allows for the possibility of a
different superfluid order parameter at every site in the lattice, such as what
has been used in previously published site-decoupled mean-field theories, but a
multi-site formulation also allows for the inclusion of spatial correlations
allowing us, e.g., to calculate the correlation length (over the length scale
of each cluster). We present our numerical results for a two-dimensional
system. This theory is shown to produce a phase diagram in which the stability
of the Mott insulator phase is larger than that predicted by site-decoupled
single-site mean-field theory. Two different methods are given for the
identification of the Bose glass-to-superfluid transition, one an approximation
based on the behaviour of the condensate fraction, and one of which relies on
obtaining the spatial variation of the order parameter correlation. The
relation of our results to a recent proposal that both transitions are non
self-averaging is discussed. | cond-mat_dis-nn |
Millisecond Electron-Phonon Relaxation in Ultrathin Disordered Metal
Films at Millikelvin Temperatures: We have measured directly the thermal conductance between electrons and
phonons in ultra-thin Hf and Ti films at millikelvin temperatures. The
experimental data indicate that electron-phonon coupling in these films is
significantly suppressed by disorder. The electron cooling time $\tau_\epsilon$
follows the $T^{-4}$-dependence with a record-long value $\tau_\epsilon=25ms$
at $T=0.04K$. The hot-electron detectors of far-infrared radiation, fabricated
from such films, are expected to have a very high sensitivity. The noise
equivalent power of a detector with the area $1\mum^2$ would be
$(2-3)10^{-20}W/Hz^{1/2}$, which is two orders of magnitude smaller than that
of the state-of-the-art bolometers. | cond-mat_dis-nn |
Relation of the thermodynamic parameter of disordering with the width of
structure factor and defect concentration in a metallic glass: In this work, we show that above the glass transition there exists a strong
unique interrelationship between the thermodynamic parameter of disorder of a
metallic glass derived using its excess entropy, diffraction measure of
disorder given by the width of the X-ray structure factor and defect
concentration derived from shear modulus measurements. Below the glass
transition, this relationship is more complicated and depends on both
temperature and thermal prehistory. | cond-mat_dis-nn |
A method of effective potentials for calculating the frequency spectrum
of eccentrically layered spherical cavity resonators: A novel method for the calculation of eigenfrequencies of non-uniformly
filled spherical cavity resonators is developed. The impact of the system
symmetry on the electromagnetic field distribution as well as on its degrees of
freedom (the set of resonant modes) is examined. It is shown that in the case
of angularly symmetric cavity, regardless of its radial non-uniformity, the set
of resonator modes is, as anticipated, a superposition of TE and TM
oscillations which can be described in terms of a single scalar function
independently of each other. The spectrum is basically determined through the
introduction of effective ``dynamic'' potentials which encode the infill
inhomogeneity. The violation of polar symmetry in the infill dielectric
properties, the azimuthal symmetry being simultaneously preserved, suppresses
all azimuthally non-uniform modes of electric-type (TM) oscillations. In the
absence of angular symmetry of both electric and magnetic properties of the
resonator infill, only azimuthally uniform distribution of both TM and TE
fields is expected to occur in the resonator. The comparison is made of the
results obtained through the proposed method and of the test problem solution
obtained with use of commercial solvers. The method appears to be efficient for
computational complex algorithms for solving spectral problems, including those
for studying the chaotic properties of electrodynamic systems' spectra. | cond-mat_dis-nn |
Long-range influence of manipulating disordered-insulators locally: Localization of wavefunctions is arguably the most familiar effect of
disorder in quantum systems. It has been recently argued [[V. Khemani, R.
Nandkishore, and S. L. Sondhi, Nature Physics, 11, 560 (2015)] that, contrary
to naive expectation, manipulation of a localized-site in the disordered medium
may produce a disturbance over a length-scale much larger than the
localization-length $\xi$. Here we report on the observation of this nonlocal
phenomenon in electronic transport experiment. Being a wave property,
visibility of this effect hinges upon quantum-coherence, and its spatial-scale
may be ultimately limited by the phase-coherent length of the disordered
insulator. Evidence for quantum coherence in the Anderson-insulating phase may
be obtained from magneto-resistance measurements which however are useful
mainly in thin-films. The technique used in this work offers an empirical
method to measure this fundamental aspect of Anderson-insulators even in
relatively thick samples. | cond-mat_dis-nn |
On the shape of invading population in oriented environments: We analyze the properties of population spreading in environments with
spatial anisotropy within the frames of a lattice model of asymmetric (biased)
random walkers. The expressions for the universal shape characteristics of the
instantaneous configuration of population, such as asphericity $A$ and
prolateness $S$ are found analytically and proved to be dependent only on the
asymmetric transition probabilities in different directions. The model under
consideration is shown to capture, in particular, the peculiarities of invasion
in presence of an array of oriented tubes (fibers) in the environment. | cond-mat_dis-nn |
Carrier induced ferromagnetism in diluted local-moment systems: The electronic and magnetic properties of concentrated and diluted
ferromagnetic semiconductors are investigated by using the Kondo lattice model,
which describes an interband exchange coupling between itinerant conduction
electrons and localized magnetic moments. In our calculations, the electronic
problem and the local magnetic problem are solved separately. For the
electronic part an interpolating self-energy approach together with a coherent
potential approximation (CPA) treatment of a dynamical alloy analogy is used to
calculate temperature-dependent quasiparticle densities of states and the
electronic self-energy of the diluted local-moment system. For constructing the
magnetic phase diagram we use a modified RKKY theory by mapping the interband
exchange to an effective Heisenberg model. The exchange integrals appear as
functionals of the diluted electronic self-energy being therefore temperature-
and carrier-concentration-dependent and covering RKKY as well as double
exchange behavior. The disorder of the localized moments in the effective
Heisenberg model is solved by a generalized locator CPA approach. The main
results are: 1) extremely low carrier concentrations are sufficient to induce
ferromagnetism; 2) the Curie temperature exhibits a strikingly non-monotonic
behavior as a function of carrier concentration with a distinct maximum; 3)
$T_C$ curves break down at critical $n/x$ due to antiferromagnetic correlations
and 4) the dilution always lowers $T_C$ but broadens the ferromagnetic region
with respect to carrier concentration. | cond-mat_dis-nn |
Instability of speckle patterns in random media with noninstantaneous
Kerr nonlinearity: Onset of the instability of a multiple-scattering speckle pattern in a random
medium with Kerr nonlinearity is significantly affected by the noninstantaneous
character of the nonlinear medium response. The fundamental time scale of the
spontaneous speckle dynamics beyond the instability threshold is set by the
largest of times $T_{\mathrm{D}}$ and $\tau_{\mathrm{NL}}$, where
$T_{\mathrm{D}}$ is the time required for the multiple-scattered waves to
propagate through the random sample and $\tau_{\mathrm{NL}}$ is the relaxation
time of the nonlinearity. Inertial nature of the nonlinearity should complicate
the experimental observation of the instability phenomenon. | cond-mat_dis-nn |
Comment on "Evidence for nontrivial ground-state structure of 3d +/- J
spin glasses": In a recent Letter [Europhys. Lett. 40, 429 (1997)], Hartmann presented
results for the structure of the degenerate ground states of the
three-dimensional +/- J spin glass model obtained using a genetic algorithm. In
this Comment, I argue that the method does not produce the correct
thermodynamic distribution of ground states and therefore gives erroneous
results for the overlap distribution. I present results of simulated annealing
calculations using different annealing rates for cubic lattices with
N=4*4*4spins. The disorder-averaged overlap distribution exhibits a significant
dependence on the annealing rate, even when the energy has converged. For fast
annealing, moments of the distribution are similar to those presented by
Hartmann. However, as the annealing rate is lowered, they approach the results
previously obtained using a multi-canonical Monte Carlo method. This shows
explicitly that care must be taken not only to reach states with the lowest
energy but also to ensure that they obey the correct thermodynamic
distribution, i.e., that the probability is the same for reaching any of the
ground states. | cond-mat_dis-nn |
Phase Transition in Multiprocessor Scheduling: The problem of distributing the workload on a parallel computer to minimize
the overall runtime is known as Multiprocessor Scheduling Problem. It is
NP-hard, but like many other NP-hard problems, the average hardness of random
instances displays an ``easy-hard'' phase transition. The transition in
Multiprocessor Scheduling can be analyzed using elementary notions from
crystallography (Bravais lattices) and statistical mechanics (Potts vectors).
The analysis reveals the control parameter of the transition and its critical
value including finite size corrections. The transition is identified in the
performance of practical scheduling algorithms. | cond-mat_dis-nn |
Simple models of small world networks with directed links: We investigate the effect of directed short and long range connections in a
simple model of small world network. Our model is such that we can determine
many quantities of interest by an exact analytical method. We calculate the
function $V(T)$, defined as the number of sites affected up to time $T$ when a
naive spreading process starts in the network. As opposed to shortcuts, the
presence of un-favorable bonds has a negative effect on this quantity. Hence
the spreading process may not be able to affect all the network. We define and
calculate a quantity named the average size of accessible world in our model.
The interplay of shortcuts, and un-favorable bonds on the small world
properties is studied. | cond-mat_dis-nn |
Potts Glass on Random Graphs: We solve the q-state Potts model with anti-ferromagnetic interactions on
large random lattices of finite coordination. Due to the frustration induced by
the large loops and to the local tree-like structure of the lattice this model
behaves as a mean field spin glass. We use the cavity method to compute the
temperature-coordination phase diagram and to determine the location of the
dynamic and static glass transitions, and of the Gardner instability. We show
that for q>=4 the model possesses a phenomenology similar to the one observed
in structural glasses. We also illustrate the links between the positive and
the zero-temperature cavity approaches, and discuss the consequences for the
coloring of random graphs. In particular we argue that in the colorable region
the one-step replica symmetry breaking solution is stable towards more steps of
replica symmetry breaking. | cond-mat_dis-nn |
Depinning in a two-layer model of plastic flow: We study a model of two layers, each consisting of a d-dimensional elastic
object driven over a random substrate, and mutually interacting through a
viscous coupling. For this model, the mean-field theory (i.e. a fully connected
model) predicts a transition from elastic depinning to hysteretic plastic
depinning as disorder or viscous coupling is increased. A functional RG
analysis shows that any small inter-layer viscous coupling destablizes the
standard (decoupled) elastic depinning FRG fixed point for d <= 4, while for d
> 4 most aspects of the mean-field theory are recovered. A one-loop study at
non-zero velocity indicates, for d<4, coexistence of a moving state and a
pinned state below the elastic depinning threshold, with hysteretic plastic
depinning for periodic and non-periodic driven layers. A 2-loop analysis of
quasi-statics unveils the possibility of more subtle effects, including a new
universality class for non-periodic objects. We also study the model in d=0,
i.e. two coupled particles, and show that hysteresis does not always exist as
the periodic steady state with coupled layers can be dynamically unstable. It
is also proved that stable pinned configurations remain dynamically stable in
presence of a viscous coupling in any dimension d. Moreover, the layer model
for periodic objects is stable to an infinitesimal commensurate density
coupling. Our work shows that a careful study of attractors in phase space and
their basin of attraction is necessary to obtain a firm conclusion for
dimensions d=1,2,3. | cond-mat_dis-nn |
Double-Well Optical Lattices with Atomic Vibrations and Mesoscopic
Disorder: Double-well optical lattice in an insulating state is considered. The
influence of atomic vibrations and mesoscopic disorder on the properties of the
lattice are studied. Vibrations lead to the renormalization of atomic
interactions. The occurrence of mesoscopic disorder results in the appearance
of first-order phase transitions between the states with different levels of
atomic imbalance. The existence of a nonuniform external potential, such as
trapping potential, essentially changes the lattice properties, suppressing the
disorder fraction and rising the transition temperature. | cond-mat_dis-nn |
Noncollinear magnetic order in quasicrystals: Based on Monte-Carlo simulations, the stable magnetization configurations of
an antiferromagnet on a quasiperiodic tiling are derived theoretically. The
exchange coupling is assumed to decrease exponentially with the distance
between magnetic moments. It is demonstrated that the superposition of
geometric frustration with the quasiperiodic ordering leads to a
three-dimensional noncollinear antiferromagnetic spin structure. The structure
can be divided into several ordered interpenetrating magnetic supertilings of
different energy and characteristic wave vector. The number and the symmetry of
subtilings depend on the quasiperiodic ordering of atoms. | cond-mat_dis-nn |
The Random-Diluted Triangular Plaquette Model: study of phase
transitions in a Kinetically Constrained Model: We study how the thermodynamic properties of the Triangular Plaquette Model
(TPM) are influenced by the addition of extra interactions. The thermodynamics
of the original TPM is trivial, while its dynamics is glassy, as usual in
Kinetically Constrained Models. As soon as we generalize the model to include
additional interactions, a thermodynamic phase transition appears in the
system. The additional interactions we consider are either short ranged,
forming a regular lattice in the plane, or long ranged of the small-world kind.
In the case of long-range interactions we call the new model Random-Diluted
TPM. We provide arguments that the model so modified should undergo a
thermodynamic phase transition, and that in the long-range case this is a glass
transition of the "Random First-Order" kind. Finally, we give support to our
conjectures studying the finite temperature phase diagram of the Random-Diluted
TPM in the Bethe approximation. This corresponds to the exact calculation on
the random regular graph, where free-energy and configurational entropy can be
computed by means of the cavity equations. | cond-mat_dis-nn |
Ideal strength of random alloys from first-principles theory: The all-electron exact muffin-tin orbitals method in combination with the
coherent-potential appproximation has been employed to investigate the ideal
tensile strengths of elemental V, Mo solids and V- and Mo-based random solid
solutions. The present ideal tensile strengths, calculated assuming isotropic
Poisson contraction, are 16.1, 26.7 and 37.6 GPa for bcc V in the [001], [111]
and [110] directions, respectively, and 26.7 GPa for bcc Mo in the [001]
direction, which are all in good agreement with the available theoretical data.
When a few percent Tc is introduced in Mo, it is found that the ideal strength
decreases in the [001] direction. For the V-based alloys, Cr increases and Ti
decreases the ideal tensile strength in all principal directions. Adding the
same concentration of Cr and Ti to V leads to ternary alloys with similar ideal
strength values as that of pure V. The alloying effects on the ideal strength
is explained using the electronic band structure. | cond-mat_dis-nn |
Aging is - almost - like equilibrium: We study and compare equilibrium and aging dynamics on both sides of the
ideal glass transition temperature $T_{MCT}$. In the context of a mean field
model, we observe that all dynamical behaviors are determined by the energy
distance $\epsilon$ to threshold - i.e. marginally stable - states. We
furthermore show the striking result that after eliminating age and temperature
at the benefit of $\epsilon$, the scaling behaviors above and below $T_{MCT}$
are identical, reconciling {\it en passant} the mean field results with
experimental observations. In the vicinity of the transition, we show that
there is an exact mapping between equilibrium dynamics and aging dynamics. This
leads to very natural interpretations and quantitative predictions for several
remarkable features of aging dynamics: waiting time-temperature superposition,
interrupted aging, dynamical heterogeneity. | cond-mat_dis-nn |
Incorrect sample classification in "Electron localization induced by
intrinsic anion disorder in a transition metal oxynitride": In the recent study of the metal-insulator transition (MIT) in the disordered
crystalline solid SrNbO$_{3-x}$N$_x$ by Daichi Oka et al. [Commun. Phys. 4, 269
(2021)], the data evaluation relies on the Al'tshuler-Aronov theory of the
interference of electron-electron interaction and elastic impurity scattering
of electrons. The present comment shows that this evaluation approach is
inappropriate. For that aim, we reconsider data for the samples with $x = 0.96$
and $x = 1.02$ from three different perspectives: (i) analysis of the
logarithmic temperature derivative of the conductivity, (ii) study of the
deviations of the measured conductivity data from the Al'tshuler-Aronov
approximation of the temperature dependence, and (iii) comparison of the
measured temperature data with the values obtained treating the sample as
secondary thermometer in terms of that approximation.
This way, for the sample with $x = 0.96$, classified as metallic by Daichi
Oka et al., qualitative contradictions between the measurements and the
zero-temperature extrapolation according to the Al'tshuler-Aronov theory are
uncovered. Thus, this sample very likely exhibits activated instead of metallic
conduction. In consequence, our findings question the continuity of the MIT
resulting from the highly cited scaling theory of localization. | cond-mat_dis-nn |
Random-field-induced disordering mechanism in a disordered ferromagnet:
Between the Imry-Ma and the standard disordering mechanism: Random fields disorder Ising ferromagnets by aligning single spins in the
direction of the random field in three space dimensions, or by flipping large
ferromagnetic domains at dimensions two and below. While the former requires
random fields of typical magnitude similar to the interaction strength, the
latter Imry-Ma mechanism only requires infinitesimal random fields. Recently,
it has been shown that for dilute anisotropic dipolar systems a third mechanism
exists, where the ferromagnetic phase is disordered by finite-size glassy
domains at a random field of finite magnitude that is considerably smaller than
the typical interaction strength. Using large-scale Monte Carlo simulations and
zero-temperature numerical approaches, we show that this mechanism applies to
disordered ferromagnets with competing short-range ferromagnetic and
antiferromagnetic interactions, suggesting its generality in ferromagnetic
systems with competing interactions and an underlying spin-glass phase. A
finite-size-scaling analysis of the magnetization distribution suggests that
the transition might be first order. | cond-mat_dis-nn |
High-dimensional order parameters and neural network classifiers applied
to amorphous ices: Amorphous ice phases are key constituents of water's complex structural
landscape. This study investigates the polyamorphic nature of water, focusing
on the complexities within low-density amorphous ice (LDA), high-density
amorphous ice (HDA), and the recently discovered medium-density amorphous ice
(MDA). We use rotationally-invariant, high-dimensional order parameters to
capture a wide spectrum of local symmetries for the characterisation of local
oxygen environments. We train a neural network (NN) to classify these local
environments, and investigate the distinctiveness of MDA within the structural
landscape of amorphous ice. Our results highlight the difficulty in accurately
differentiating MDA from LDA due to structural similarities. Beyond water, our
methodology can be applied to investigate the structural properties and phases
of disordered materials. | cond-mat_dis-nn |
Bistable Gradient Networks II: Storage Capacity and Behaviour Near
Saturation: We examine numerically the storage capacity and the behaviour near saturation
of an attractor neural network consisting of bistable elements with an
adjustable coupling strength, the Bistable Gradient Network (BGN). For strong
coupling, we find evidence of a first-order "memory blackout" phase transition
as in the Hopfield network. For weak coupling, on the other hand, there is no
evidence of such a transition and memorized patterns can be stable even at high
levels of loading. The enhanced storage capacity comes, however, at the cost of
imperfect retrieval of the patterns from corrupted versions. | cond-mat_dis-nn |
Vortex characterisation of frustration in the 2d Ising spin glass: The frustrated Ising model on a two-dimensional lattice with open boundary
conditions is revisited. A hidden Z2 gauge symmetry relates models with
different frustrations which, however, share the same partition function. By
means of a duality transformation, it is shown that the partition function only
depends on the distribution of gauge invariant vortices on the lattice. We
finally show that the exact ground state energy can be calculated in polynomial
time using Edmonds' algorithm. | cond-mat_dis-nn |
Correlation between vibrational anomalies and emergent anharmonicity of
local potential energy landscape in metallic glasses: The boson peak (BP) is a universal feature in the Raman and inelastic
scattering spectra of both disordered and crystalline materials. The current
paradigm presents the boson peak as the result of a Ioffe-Regel crossover
between ballistic (phonon) and diffusive-type excitations, where the loss of
coherence of phonons is described as a purely harmonic process due to
structural disorder. This "harmonic disorder" paradigm for the BP has never
been challenged or tested at the atomistic level. Here, through a set of
atomistically-resolved characterizations of amorphous metallic alloys, we
uncover a robust inverse proportionality between the intensity of boson peak
and the activation energy of excitations in the potential energy landscape
(PEL). Larger boson peak is linked with shallower basins and lower activation
barriers and, consequently, with strongly anharmonic sectors of the PEL.
Numerical evidence from atomistic simulations indicates that THz atomic
vibrations contributing the most to the BP in atomic glasses are strongly
anharmonic, as evidenced through very large values of the atomic- and
mode-resolved Gr\"{u}neisen parameter found for the atomic vibrations that
constitute the BP. These results provide a direct bridge between the
vibrational spectrum and the topology of the PEL in solids, and point towards a
new "giant anharmonicity" paradigm for both generic disordered materials and
for the phonon-glass problem in emerging materials for energy applications. In
this sense, disorder and anharmonicity emerge as the two sides of the same
coin. | cond-mat_dis-nn |
Understanding the problem of glass transition on the basis of elastic
waves in a liquid: We propose that the properties of glass transition can be understood on the
basis of elastic waves. Elastic waves originating from atomic jumps in a liquid
propagate local expansion due to the anharmonicity of interatomic potential.
This creates dynamic compressive stress, which increases the activation barrier
for other events in a liquid. The non-trivial point is that the range of
propagation of high-frequency elastic waves, $d_{\rm el}$, increases with
liquid relaxation time $\tau$. A self-consistent calculation shows that this
increase gives the Vogel-Fulcher-Tammann (VFT) law. In the proposed theory, we
discuss the origin of two dynamic crossovers in a liquid: 1) the crossover from
exponential to non-exponential and from Arrhenius to VFT relaxation at high
temperature and 2) the crossover from the VFT to a more Arrhenius-like
relaxation at low temperature. The corresponding values of $\tau$ at the two
crossovers are in quantitative parameter-free agreement with experiments. The
origin of the second crossover allows us to reconcile the ongoing controversy
surrounding the possible divergence of $\tau$. The crossover to Arrhenius
relaxation universally takes place when $d_{\rm el}$ reaches system size, thus
avoiding divergence and associated theoretical complications such as
identifying the nature of the phase transition and the second phase itself.
Finally, we discuss the effect of volume on $\tau$ and the origin of liquid
fragility. | cond-mat_dis-nn |
Photocount statistics in mesoscopic optics: We report the first observation of the impact of mesoscopic fluctuations on
the photocount statistics of coherent light scattered in a random medium.
Poisson photocount distribution of the incident light widens and gains
additional asymmetry upon transmission through a suspension of small dielectric
spheres. The effect is only appreciable when the average number <n> of
photocounts becomes comparable or larger than the effective dimensionless
conductance g of the sample. | cond-mat_dis-nn |
Strain localisation above the yielding point in cyclically deformed
glasses: We study the yielding behaviour of a model glass under cyclic athermal
quastistatic deformation computationally, and show that yielding is
characterised by the discontinuous appearance of shear bands, whose width is
about ten particle diameters at their initiation, in which the strain gets
localised. Strain localisation is accompanied by a corresponding change in the
energies, and a decrease in the density in the shear band. We show that the
glass remains well annealed outside the shear band whereas the energies
correspond to the highest possible energy minima at the given density within
the shear band. Diffusive motion of particles characterising the yielded state
are confined to the shear bands, whose mean positions display movement over
repeated cycles. Outside the shear band, particle motions are sub-diffusive but
remain finite. Despite the discontinuous nature of their appearance, shear
bands are reversible in the sense that a reduction in the amplitude of cyclic
deformation to values below yielding leads to the healing and disappearance of
the shear bands. | cond-mat_dis-nn |
Glass and jamming transition of simple liquids: static and dynamic
theory: We study the glass and jamming transition of finite-dimensional models of
simple liquids: hard- spheres, harmonic spheres and more generally bounded pair
potentials that modelize frictionless spheres in interaction. At finite
temperature, we study their glassy dynamics via field-theoretic methods by
resorting to a mapping towards an effective quantum mechanical evolution, and
show that such an approach resolves several technical problems encountered with
previous attempts. We then study the static, mean-field version of their glass
transition via replica theory, and set up an expansion in terms of the
corresponding static order parameter. Thanks to this expansion, we are able to
make a direct and exact comparison between historical Mode-Coupling results and
replica theory. Finally we study these models at zero temperature within the
hypotheses of the random-first-order-transition theory, and are able to derive
a quantitative mean-field theory of the jamming transition. The theoretic
methods of field theory and liquid theory used in this work are presented in a
mostly self-contained, and hopefully pedagogical, way. This manuscript is a
corrected version of my PhD thesis, defended in June, 29th, under the
advisorship of Fr\'ed\'eric van Wijland, and also contains the result of
collaborations with Ludovic Berthier and Francesco Zamponi. The PhD work was
funded by a CFM-JP Aguilar grant, and conducted in the Laboratory MSC at
Universit\'e Denis Diderot--Paris 7, France. | cond-mat_dis-nn |
Relation between heterogeneous frozen regions in supercooled liquids and
non-Debye spectrum in the corresponding glasses: Recent numerical studies on glassy systems provide evidences for a population
of non-Goldstone modes (NGMs) in the low-frequency spectrum of the vibrational
density of states $D(\omega)$. Similarly to Goldstone modes (GMs), i. e.,
phonons in solids, NGMs are soft low-energy excitations. However, differently
from GMs, NGMs are localized excitations. Here we first show that the parental
temperature $T^*$ modifies the GM/NGM ratio in $D(\omega)$. In particular, the
phonon attenuation is reflected in a parental temperature dependency of the
exponent $s(T^*)$ in the low-frequency power law $D(\omega) \sim
\omega^{s(T^*)}$, with $2 \leq s(T^*) \leq 4 $. Secondly, by comparing $s(T^*)$
with $s(p)$, i. e., the same quantity obtained by pinning \mttp{a} $p$ particle
fraction, we suggest that $s(T^*)$ reflects the presence of dynamical
heterogeneous regions of size $\xi^3 \propto p$. Finally, we provide an
estimate of $\xi$ as a function of $T^*$, finding a mild power law divergence,
$\xi \sim (T^* - T_d)^{-\alpha/3}$, with $T_d$ the dynamical crossover
temperature and $\alpha$ falling in the range $\alpha \in [0.8,1.0]$. | cond-mat_dis-nn |
Localization dynamics in a centrally coupled system: In systems where interactions couple a central degree of freedom and a bath,
one would expect signatures of the bath's phase to be reflected in the dynamics
of the central degree of freedom. This has been recently explored in connection
with many-body localized baths coupled with a central qubit or a single cavity
mode -- systems with growing experimental relevance in various platforms. Such
models also have an interesting connection with Floquet many-body localization
via quantizing the external drive, although this has been relatively
unexplored. Here we adapt the multilayer multiconfigurational time-dependent
Hartree (ML-MCTDH) method, a well-known tree tensor network algorithm, to
numerically simulate the dynamics of a central degree of freedom, represented
by a $d$-level system (qudit), coupled to a disordered interacting 1D spin
bath. ML-MCTDH allows us to reach $\approx 10^2$ lattice sites, a far larger
system size than what is feasible with exact diagonalization or kernel
polynomial methods. From the intermediate time dynamics, we find a well-defined
thermodynamic limit for the qudit dynamics upon appropriate rescaling of the
system-bath coupling. The spin system shows similar scaling collapse in the
Edward-Anderson spin glass order parameter or entanglement entropy at
relatively short times. At longer time scales, we see slow growth of the
entanglement, which may arise from dephasing mechanisms in the localized system
or long-range interactions mediated by the central degree of freedom. Similar
signs of localization are shown to appear as well with unscaled system-bath
coupling. | cond-mat_dis-nn |
Ordering temperatures of Ising Spin Glasses: Exploiting an approach due to Singh and Fisher I show that in the high
dimension limit the ordering temperature of near neighbour Ising Spin Glasses
drops linearly with the kurtosis of the interaction distribution, in excellent
agreement with accurate high temperature series data of Daboul, Chang and
Aharony. At lower dimensions the linear relation no longer applies strictly but
the kurtosis can still be taken to be an appropriate parameter for ranking
different systems. I also compare the series estimates with simulation and
Migdal-Kadanoff estimates where these are available. | cond-mat_dis-nn |
Roughness and critical force for depinning at 3-loop order: A $d$-dimensional elastic manifold at depinning is described by a
renormalized field theory, based on the Functional Renormalization Group (FRG).
Here we analyze this theory to 3-loop order, equivalent to third order in
$\epsilon=4-d$, where $d$ is the internal dimension. The critical exponent
reads $\zeta = \frac \epsilon3 + 0.04777 \epsilon^2 -0.068354 \epsilon^3 +
{\cal O}(\epsilon^4)$. Using that $\zeta(d=0)=2^-$, we estimate
$\zeta(d=1)=1.266(20)$, $\zeta(d=2)=0.752(1)$ and $\zeta(d=3)=0.357(1)$. For
Gaussian disorder, the pinning force per site is estimated as $f_{\rm c}= {\cal
B} m^{2}\rho_m + f_{\rm c}^0$, where $m^2$ is the strength of the confining
potential, $\cal B$ a universal amplitude, $\rho_m$ the correlation length of
the disorder, and $f_{\rm c}^0$ a non-universal lattice dependent term. For
charge-density waves, we find a mapping to the standard $\phi^4$-theory with
$O(n)$ symmetry in the limit of $n\to -2$. This gives $f_{\rm c} = \tilde {\cal
A}(d) m^2 \ln (m) + f_{\rm c}^0 $, with $\tilde {\cal A}(d) = -\partial_n
\big[\nu(d,n)^{-1}+\eta(d,n)\big]_{n=-2}$, reminiscent of log-CFTs. | cond-mat_dis-nn |
Spectral statistics across the many-body localization transition: The many-body localization transition (MBLT) between ergodic and many-body
localized phase in disordered interacting systems is a subject of much recent
interest. Statistics of eigenenergies is known to be a powerful probe of
crossovers between ergodic and integrable systems in simpler examples of
quantum chaos. We consider the evolution of the spectral statistics across the
MBLT, starting with mapping to a Brownian motion process that analytically
relates the spectral properties to the statistics of matrix elements. We
demonstrate that the flow from Wigner-Dyson to Poisson statistics is a
two-stage process. First, fractal enhancement of matrix elements upon
approaching the MBLT from the metallic side produces an effective power-law
interaction between energy levels, and leads to a plasma model for level
statistics. At the second stage, the gas of eigenvalues has local interaction
and level statistics belongs to a semi-Poisson universality class. We verify
our findings numerically on the XXZ spin chain. We provide a microscopic
understanding of the level statistics across the MBLT and discuss implications
for the transition that are strong constraints on possible theories. | cond-mat_dis-nn |
Normal and anomalous diffusion of Brownian particles on disordered
potentials: In this work we study the transition from normal to anomalous diffusion of
Brownian particles on disordered potentials. The potential model consists of a
series of "potential hills" (defined on unit cell of constant length) whose
heights are chosen randomly from a given distribution. We calculate the exact
expression for the diffusion coefficient in the case of uncorrelated potentials
for arbitrary distributions. We particularly show that when the potential
heights have a Gaussian distribution (with zero mean and a finite variance) the
diffusion of the particles is always normal. In contrast when the distribution
of the potential heights are exponentially distributed we show that the
diffusion coefficient vanishes when system is placed below a critical
temperature. We calculate analytically the diffusion exponent for the anomalous
(subdiffusive) phase by using the so-called "random trap model". We test our
predictions by means of Langevin simulations obtaining good agreement within
the accuracy of our numerical calculations. | cond-mat_dis-nn |
Robustness and Independence of the Eigenstates with respect to the
Boundary Conditions across a Delocalization-Localization Phase Transition: We focus on the many-body eigenstates across a localization-delocalization
phase transition. To characterize the robustness of the eigenstates, we
introduce the eigenstate overlaps $\mathcal{O}$ with respect to the different
boundary conditions. In the ergodic phase, the average of eigenstate overlaps
$\bar{\mathcal{O}}$ is exponential decay with the increase of the system size
indicating the fragility of its eigenstates, and this can be considered as an
eigenstate-version butterfly effect of the chaotic systems. For localized
systems, $\bar{\mathcal{O}}$ is almost size-independent showing the strong
robustness of the eigenstates and the broken of eigenstate thermalization
hypothesis. In addition, we find that the response of eigenstates to the change
of boundary conditions in many-body localized systems is identified with the
single-particle wave functions in Anderson localized systems. This indicates
that the eigenstates of the many-body localized systems, as the many-body wave
functions, may be independent of each other. We demonstrate that this is
consistent with the existence of a large number of quasilocal integrals of
motion in the many-body localized phase. Our results provide a new method to
study localized and delocalized systems from the perspective of eigenstates. | cond-mat_dis-nn |
Percolation through Voids around Overlapping Spheres, a Dynamically
based Finite Size Scaling Analysis: The percolation threshold for flow or conduction through voids surrounding
randomly placed spheres is rigorously calculated. With large scale Monte Carlo
simulations, we give a rigorous continuum treatment to the geometry of the
impenetrable spheres and the spaces between them. To properly exploit finite
size scaling, we examine multiple systems of differing sizes, with suitable
averaging over disorder, and extrapolate to the thermodynamic limit. An order
parameter based on the statistical sampling of stochastically driven dynamical
excursions and amenable to finite size scaling analysis is defined, calculated
for various system sizes, and used to determine the critical volume fraction
phi_{c} = 0.0317 +/- 0.0004 and the correlation length exponent nu = 0.92 +/-
0.05. | cond-mat_dis-nn |
Fragility and molar volumes of non-stoichiometric chalcogenides -- the
crucial role of melt/glass homogenization: Melt-fragility index (m) and glass molar volumes (Vm) of binary Ge-Se
melts/glasses are found to change reproducibly as they are homogenized.
Variance of Vm decreases as glasses homogenize, and the mean value of Vm
increases to saturate at values characteristic of homogeneous glasses. Variance
in fragility index of melts also decreases as they are homogenized, and the
mean value of m decreases to acquire values characteristic of homogeneous
melts. Broad consequences of these observations on physical behavior of
chalcogenides melts/glasses are commented upon. The intrinsically slow kinetics
of melt homogenization derives from high viscosity of select super-strong melt
compositions in the Intermediate Phase that serve to bottleneck atomic
diffusion at high temperatures. | cond-mat_dis-nn |
Recovering the state sequence of hidden Markov models using mean-field
approximations: Inferring the sequence of states from observations is one of the most
fundamental problems in Hidden Markov Models. In statistical physics language,
this problem is equivalent to computing the marginals of a one-dimensional
model with a random external field. While this task can be accomplished through
transfer matrix methods, it becomes quickly intractable when the underlying
state space is large.
This paper develops several low-complexity approximate algorithms to address
this inference problem when the state space becomes large. The new algorithms
are based on various mean-field approximations of the transfer matrix. Their
performances are studied in detail on a simple realistic model for DNA
pyrosequencing. | cond-mat_dis-nn |
Surface properties at the Kosterlitz-Thouless transition: Monte Carlo simulations of the two-dimensional XY model are performed in a
square geometry with free and mixed fixed-free boundary conditions. Using a
Schwarz-Christoffel conformal mapping, we deduce the exponent eta of the order
parameter correlation function and its surface equivalent eta_parallel at the
Kosterlitz-Thouless transition temperature. The well known value eta(T_{KT}) =
1/4 is easily recovered even with systems of relatively small sizes, since the
shape effects are encoded in the conformal mapping. The exponent associated to
the surface correlations is similarly obtained eta_1(T_{KT}) ~= 0.54. | cond-mat_dis-nn |
Universality in short-range Ising spin glasses: The role of the distribution of coupling constants on the critical exponents
of the short-range Ising spin-glass model is investigated via real space
renormalization group. A saddle-point spin glass critical point characterized
by a fixed-point distribution is found in an appropriated parameter space. The
critical exponents $\beta $ and $\nu $ are directly estimated from the data of
the local Edwards-Anderson order parameters for the model defined on a diamond
hierarchical lattice of fractal dimension $d_{f}=3$. Four distinct initial
distributions of coupling constants (Gaussian, bimodal, uniform and
exponential) are considered; the results clearly indicate a universal behavior. | cond-mat_dis-nn |
Coherent wave transmission in quasi-one-dimensional systems with Lévy
disorder: We study the random fluctuations of the transmission in disordered
quasi-one-dimensional systems such as disordered waveguides and/or quantum
wires whose random configurations of disorder are characterized by density
distributions with a long tail known as L\'evy distributions. The presence of
L\'evy disorder leads to large fluctuations of the transmission and anomalous
localization, in relation to the standard exponential localization (Anderson
localization). We calculate the complete distribution of the transmission
fluctuations for different number of transmission channels in the presence and
absence of time-reversal symmetry. Significant differences in the transmission
statistics between disordered systems with Anderson and anomalous localizations
are revealed. The theoretical predictions are independently confirmed by tight
binding numerical simulations. | cond-mat_dis-nn |
Comment on the possibility of Inverse Crystallization within van
Hemmen's Classical Spin-Glass model: In this comment, I show that van Hemmen's classical spin-glass model can also
account for processes such as inverse crystallization, where a ferromagnetic
phase appears at higher temperatures than a glass state. The so far ignored
fact is the temperature dependence of the Ruderman-Kittel-Kasuya-Yosida
interaction. This generalization may be relevant to other models. | cond-mat_dis-nn |
Broadband dielectric spectroscopy on benzophenone: alpha relaxation,
beta relaxation, and mode coupling theory: We have performed a detailed dielectric investigation of the relaxational
dynamics of glass-forming benzophenone. Our measurements cover a broad
frequency range of 0.1 Hz to 120 GHz and temperatures from far below the glass
temperature well up into the region of the small-viscosity liquid. With respect
to the alpha relaxation this material can be characterized as a typical
molecular glass former with rather high fragility. A good agreement of the
alpha relaxation behavior with the predictions of the mode coupling theory of
the glass transition is stated. In addition, at temperatures below and in the
vicinity of Tg we detect a well-pronounced beta relaxation of Johari-Goldstein
type, which with increasing temperature develops into an excess wing. We
compare our results to literature data from optical Kerr effect and depolarized
light scattering experiments, where an excess-wing like feature was observed in
the 1 - 100 GHz region. We address the question if the Cole-Cole peak, which
was invoked to describe the optical Kerr effect data within the framework of
the mode coupling theory, has any relation to the canonical beta relaxation
detected by dielectric spectroscopy. | cond-mat_dis-nn |
Moving binary Bose-Einstein condensates in a weak random potential: We study the behavior of moving Bose-Bose mixtures in a weak disordered
potential in the realm of the Bogoliubov-Huang-Meng theory. Corrections due to
the quantum fluctuations, disorder effects and the relative motion of two
fluids to the glassy fraction, the condensed depletion, the anomalous density,
and the equation of state of each species are obtained analytically for small
velocity. We show that the intriguing interplay of the relative motion and the
disorder potential could not only change the stability condition, but destroy
also the localization process in the two condensates preventing the formation
of a Bose glass state. Unexpectedly, we find that the quantum fluctuations
reduce with the velocity of the two fluids. The obtained theoretical
predictions are checked by our numerical results. | cond-mat_dis-nn |
Learning to find order in disorder: We introduce the use of neural networks as classifiers on classical
disordered systems with no spatial ordering. In this study, we implement a
convolutional neural network trained to identify the spin-glass state in the
three-dimensional Edwards-Anderson Ising spin-glass model from an input of
Monte Carlo sampled configurations at a given temperature. The neural network
is designed to be flexible with the input size and can accurately perform
inference over a small sample of the instances in the test set. Using the
neural network to classify instances of the three-dimensional Edwards-Anderson
Ising spin-glass in a (random) field we show that the inferred phase boundary
is consistent with the absence of an Almeida-Thouless line. | cond-mat_dis-nn |
Triviality of the Ground State Structure in Ising Spin Glasses: We investigate the ground state structure of the three-dimensional Ising spin
glass in zero field by determining how the ground state changes in a fixed
finite block far from the boundaries when the boundary conditions are changed.
We find that the probability of a change in the block ground state
configuration tends to zero as the system size tends to infinity. This
indicates a trivial ground state structure, as predicted by the droplet theory.
Similar results are also obtained in two dimensions. | cond-mat_dis-nn |
Barkhausen noise in the Random Field Ising Magnet Nd$_2$Fe$_{14}$B: With sintered needles aligned and a magnetic field applied transverse to its
easy axis, the rare-earth ferromagnet Nd$_2$Fe$_{14}$B becomes a
room-temperature realization of the Random Field Ising Model. The transverse
field tunes the pinning potential of the magnetic domains in a continuous
fashion. We study the magnetic domain reversal and avalanche dynamics between
liquid helium and room temperatures at a series of transverse fields using a
Barkhausen noise technique. The avalanche size and energy distributions follow
power-law behavior with a cutoff dependent on the pinning strength dialed in by
the transverse field, consistent with theoretical predictions for Barkhausen
avalanches in disordered materials. A scaling analysis reveals two regimes of
behavior: one at low temperature and high transverse field, where the dynamics
are governed by the randomness, and the second at high temperature and low
transverse field where thermal fluctuations dominate the dynamics. | cond-mat_dis-nn |
Renormalization-Group Theory of 1D quasiperiodic lattice models with
commensurate approximants: We develop a renormalization group (RG) description of the localization
properties of onedimensional (1D) quasiperiodic lattice models. The RG flow is
induced by increasing the unit cell of subsequent commensurate approximants.
Phases of quasiperiodic systems are characterized by RG fixed points associated
with renormalized single-band models. We identify fixed-points that include
many previously reported exactly solvable quasiperiodic models. By classifying
relevant and irrelevant perturbations, we show that phase boundaries of more
generic models can be determined with exponential accuracy in the approximant's
unit cell size, and in some cases analytically. Our findings provide a unified
understanding of widely different classes of 1D quasiperiodic systems. | cond-mat_dis-nn |
Band-center metal-insulator transition in bond-disordered graphene: We study the transport properties of a tight-binding model of non-interacting
fermions with random hopping on the honeycomb lattice. At the particle-hole
symmetric chemical potential, the absence of diagonal disorder (random onsite
potentials) places the system in the well-studied chiral orthogonal
universality class of disordered fermion problems, which are known to exhibit
both a critical metallic phase and a dimerization-induced localized phase.
Here, our focus is the behavior of the two-terminal conductance and the
Lyapunov spectrum in quasi-1D geometry near the dimerization-driven transition
from the metallic to the localized phase. For a staggered dimerization pattern
on the square and honeycomb lattices, we find that the renormalized
localization length $\xi/M$ ($M$ denotes the width of the sample) and the
typical conductance display scaling behavior controlled by a crossover
length-scale that diverges with exponent $\nu \approx 1.05(5)$ as the critical
point is approached. However, for the plaquette dimerization pattern, we
observe a relatively large exponent $\nu \approx 1.55(5)$ revealing an apparent
non-universality of the delocalization-localization transition in the BDI
symmetry class. | cond-mat_dis-nn |
Dynamics of a quantum phase transition in the Aubry-André-Harper
model with $p$-wave superconductivity: We investigate the nonequilibrium dynamics of the one-dimension
Aubry-Andr\'{e}-Harper model with $p$-wave superconductivity by changing the
potential strength with slow and sudden quench. Firstly, we study the slow
quench dynamics from localized phase to critical phase by linearly decreasing
the potential strength $V$. The localization length is finite and its scaling
obeys the Kibble-Zurek mechanism. The results show that the second-order phase
transition line shares the same critical exponent $z\nu$, giving the
correlation length $\nu=0.997$ and dynamical exponent $z=1.373$, which are
different from the Aubry-Andr\'{e} model. Secondly, we also study the sudden
quench dynamics between three different phases: localized phase, critical
phase, and extended phase. In the limit of $V=0$ and $V=\infty$, we
analytically study the sudden quench dynamics via the Loschmidt echo. The
results suggest that, if the initial state and the post-quench Hamiltonian are
in different phases, the Loschmidt echo vanishes at some time intervals.
Furthermore, we found that, if the initial value is in the critical phase, the
direction of the quench is the same as one of the two limits mentioned before,
and similar behaviors will occur. | cond-mat_dis-nn |
Coulomb Glasses: A Comparison Between Mean Field and Monte Carlo Results: Recently a local mean field theory for both eqilibrium and transport
properties of the Coulomb glass was proposed [A. Amir et al., Phys. Rev. B 77,
165207 (2008); 80, 245214 (2009)]. We compare the predictions of this theory to
the results of dynamic Monte Carlo simulations. In a thermal equilibrium state
we compare the density of states and the occupation probabilities. We also
study the transition rates between different states and find that the mean
field rates underestimate a certain class of important transitions. We propose
modified rates to be used in the mean field approach which take into account
correlations at the minimal level in the sense that transitions are only to
take place from an occupied to an empty site. We show that this modification
accounts for most of the difference between the mean field and Monte Carlo
rates. The linear response conductance is shown to exhibit the Efros-Shklovskii
behaviour in both the mean field and Monte Carlo approaches, but the mean field
method strongly underestimates the current at low temperatures. When using the
modified rates better agreement is achieved. | cond-mat_dis-nn |
Spin Wave Propagation in the Domain State of a Random Field Magnet: Inelastic neutron scattering with high wave-vector resolution has
characterized the propagation of transverse spin wave modes near the
antiferromagnetic zone center in the metastable domain state of a random field
Ising magnet. A well-defined, long wavelength excitation is observed despite
the absence of long-range magnetic order. Direct comparisons with the spin wave
dispersion in the long-range ordered antiferromagnetic state reveal no
measurable effects from the domain structure. This result recalls analogous
behavior in thermally disordered anisotropic spin chains but contrasts sharply
with that of the phonon modes in relaxor ferroelectrics. | cond-mat_dis-nn |
On the Approach to the Equilibrium and the Equilibrium Properties of a
Glass-Forming Model: In this note we apply some theoretical predictions that arise in the mean
field framework for a large class of infinite range models to structural
glasses and we present a first comparison of these predictions with numerical
results. | cond-mat_dis-nn |
A Simple Model for Simple Aging in Glassy Yttrium-Hydrides: A simple explanation for the logarithmic aging of the photoconductivity in
yttriumhydride is proposed. We show that the scaling (``simple'' aging) of the
relaxation response with the illumination time t_w is consistent with the
superposition of independently relaxing excitations with time offsets
distributed over a window of width t_w. | cond-mat_dis-nn |
Pinning dependent field driven domain wall dynamics and thermal scaling
in an ultrathin Pt/Co/Pt magnetic film: Magnetic field-driven domain wall motion in an ultrathin Pt/Co(0.45nm)/Pt
ferromagnetic film with perpendicular anisotropy is studied over a wide
temperature range. Three different pinning dependent dynamical regimes are
clearly identified: the creep, the thermally assisted flux flow and the
depinning, as well as their corresponding crossovers. The wall elastic energy
and microscopic parameters characterizing the pinning are determined. Both the
extracted thermal rounding exponent at the depinning transition, $\psi=$0.15,
and the Larkin length crossover exponent, $\phi=$0.24, fit well with the
numerical predictions. | cond-mat_dis-nn |
Entropy and typical properties of Nash equilibria in two-player games: We use techniques from the statistical mechanics of disordered systems to
analyse the properties of Nash equilibria of bimatrix games with large random
payoff matrices. By means of an annealed bound, we calculate their number and
analyse the properties of typical Nash equilibria, which are exponentially
dominant in number. We find that a randomly chosen equilibrium realizes almost
always equal payoffs to either player. This value and the fraction of
strategies played at an equilibrium point are calculated as a function of the
correlation between the two payoff matrices. The picture is complemented by the
calculation of the properties of Nash equilibria in pure strategies. | cond-mat_dis-nn |
Learning and inference in a nonequilibrium Ising model with hidden nodes: We study inference and reconstruction of couplings in a partially observed
kinetic Ising model. With hidden spins, calculating the likelihood of a
sequence of observed spin configurations requires performing a trace over the
configurations of the hidden ones. This, as we show, can be represented as a
path integral. Using this representation, we demonstrate that systematic
approximate inference and learning rules can be derived using dynamical
mean-field theory. Although naive mean-field theory leads to an unstable
learning rule, taking into account Gaussian corrections allows learning the
couplings involving hidden nodes. It also improves learning of the couplings
between the observed nodes compared to when hidden nodes are ignored. | cond-mat_dis-nn |
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