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Hyperscaling breakdown and Ising Spin Glasses: the Binder cumulant: Among the Renormalization Group Theory scaling rules relating critical
exponents, there are hyperscaling rules involving the dimension of the system.
It is well known that in Ising models hyperscaling breaks down above the upper
critical dimension. It was shown by M. Schwartz [Europhys. Lett. {\bf 15}, 777
(1991)] that the standard Josephson hyperscaling rule can also break down in
Ising systems with quenched random interactions. A related Renormalization
Group Theory hyperscaling rule links the critical exponents for the normalized
Binder cumulant and the correlation length in the thermodynamic limit. An
appropriate scaling approach for analyzing measurements from criticality to
infinite temperature is first outlined. Numerical data on the scaling of the
normalized correlation length and the normalized Binder cumulant are shown for
the canonical Ising ferromagnet model in dimension three where hyperscaling
holds, for the Ising ferromagnet in dimension five (so above the upper critical
dimension) where hyperscaling breaks down, and then for Ising spin glass models
in dimension three where the quenched interactions are random. For the Ising
spin glasses there is a breakdown of the normalized Binder cumulant
hyperscaling relation in the thermodynamic limit regime, with a return to size
independent Binder cumulant values in the finite-size scaling regime around the
critical region. | cond-mat_dis-nn |
Closed-Form Density of States and Localization Length for a
Non-Hermitian Disordered System: We calculate the Lyapunov exponent for the non-Hermitian Zakharov-Shabat
eigenvalue problem corresponding to the attractive non-linear Schroedinger
equation with a Gaussian random pulse as initial value function. Using an
extension of the Thouless formula to non-Hermitian random operators, we
calculate the corresponding average density of states. We analyze two cases,
one with circularly symmetric complex Gaussian pulses and the other with real
Gaussian pulses. We discuss the implications in the context of the information
transmission through non-linear optical fibers. | cond-mat_dis-nn |
Intrinsic versus super-rough anomalous scaling in spontaneous imbibition: We study spontaneous imbibition using a phase field model in a two
dimensional system with a dichotomic quenched noise. By imposing a constant
pressure $\mu_{a}<0$ at the origin, we study the case when the interface
advances at low velocities, obtaining the scaling exponents $z=3.0\pm 0.1$,
$\alpha=1.50\pm 0.02$ and $\alpha_{loc}= 0.95\pm 0.03$ within the intrinsic
anomalous scaling scenario. These results are in quite good agreement with
experimental data recently published. Likewise, when we increase the interface
velocity, the resulting scaling exponents are $z=4.0 \pm 0.1$, $\alpha=1.25\pm
0.02$ and $\alpha_{loc}= 0.95\pm 0.03$. Moreover, we observe that the local
properties of the interface change from a super-rough to an intrinsic anomalous
description when the contrast between the two values of the dichotomic noise is
increased. From a linearized interface equation we can compute analytically the
global scaling exponents which are comparable to the numerical results,
introducing some properties of the quenched noise. | cond-mat_dis-nn |
Spatial Structures of Anomalously Localized States in Tail Regions at
the Anderson Transition: We study spatial structures of anomalously localized states (ALS) in tail
regions at the critical point of the Anderson transition in the two-dimensional
symplectic class. In order to examine tail structures of ALS, we apply the
multifractal analysis only for the tail region of ALS and compare with the
whole structure. It is found that the amplitude distribution in the tail region
of ALS is multifractal and values of exponents characterizing multifractality
are the same with those for typical multifractal wavefunctions in this
universality class. | cond-mat_dis-nn |
Persistence of chirality in the Su-Schrieffer-Heeger model in the
presence of on-site disorder: We consider the effects of on-site and hopping disorder on zero modes in the
Su-Schrieffer-Heeger model. In the absence of disorder a domain wall gives rise
to two chiral fractionalized bound states, one at the edge and one bound to the
domain wall. On-site disorder breaks the chiral symmetry, in contrast to
hopping disorder. By using the polarization we find that on-site disorder has
little effect on the chiral nature of the bound states for weak to moderate
disorder. We explore the behaviour of these bound states for strong disorder,
contrasting on-site and hopping disorder and connect our results to the
localization properties of the bound states and to recent experiments. | cond-mat_dis-nn |
Far-from-equilibrium criticality in the Random Field Ising Model with
Eshelby Interactions: We study a quasi-statically driven random field Ising model (RFIM) at zero
temperature with interactions mediated by the long-range anisotropic Eshelby
kernel. Analogously to amorphous solids at their yielding transition, and
differently from ferromagnetic and dipolar RFIMs, the model shows a
discontinuous magnetization jump associated with the appearance of a band-like
structure for weak disorder and a continuous magnetization growth, yet
punctuated by avalanches, for strong disorder. Through a finite-size scaling
analysis in 2 and 3 dimensions we find that the two regimes are separated by a
finite-disorder critical point which we characterize. We discuss similarities
and differences between the present model and models of sheared amorphous
solids. | cond-mat_dis-nn |
Non-Hermitian disorder in two-dimensional optical lattices: In this paper, we study the properties of two-dimensional lattices in the
presence of non-Hermitian disorder. In the context of coupled mode theory, we
consider random gain-loss distributions on every waveguide channel (on site
disorder). Our work provides a systematic study of the interplay between
disorder and non-Hermiticity. In particular, we study the eigenspectrum in the
complex frequency plane and we examine the localization properties of the
eigenstates, either by the participation ratio or the level spacing, defined in
the complex plane. A modified level distribution function vs disorder seems to
fit our computational results. | cond-mat_dis-nn |
Energy distribution of maxima and minima in a one-dimensional random
system: We study the energy distribution of maxima and minima of a simple
one-dimensional disordered Hamiltonian. We find that in systems with short
range correlated disorder there is energy separation between maxima and minima,
such that at fixed energy only one kind of stationary points is dominant in
number over the other. On the other hand, in the case of systems with long
range correlated disorder maxima and minima are completely mixed. | cond-mat_dis-nn |
Monte Carlo Simulations of Doped, Diluted Magnetic Semiconductors - a
System with Two Length Scales: We describe a Monte Carlo simulation study of the magnetic phase diagram of
diluted magnetic semiconductors doped with shallow impurities in the low
concentration regime. We show that because of a wide distribution of
interaction strengths, the system exhibits strong quantum effects in the
magnetically ordered phase. A discrete spin model, found to closely approximate
the quantum system, shows long relaxation times, and the need for specialized
cluster algorithms for updating spin configurations. Results for a
representative system are presented. | cond-mat_dis-nn |
Reply to Shvaika et al.: Presence of a boson peak in anharmonic phonon
models with Akhiezer-type damping: We reply to the Comment by Svhaika, Ruocco, Schirmacher and collaborators.
There were two accidental mistakes in our original paper (Phys. Rev. Lett. 112,
145501 (2019)), which have been now corrected. All the physical conclusions and
results of the original paper, including the prediction of boson peak due to
anharmonicity, remain valid in the corrected version. | cond-mat_dis-nn |
Analytical Approach to Noise Effects on Synchronization in a System of
Coupled Excitable Elements: We report relationships between the effects of noise and applied constant
currents on the behavior of a system of excitable elements. The analytical
approach based on the nonlinear Fokker-Planck equation of a mean-field model
allows us to study the effects of noise without approximations only by dealing
with deterministic nonlinear dynamics . We find the similarity, with respect to
the occurrence of oscillations involving subcritical Hopf bifurcations, between
the systems of an excitable element with applied constant currents and
mean-field coupled excitable elements with noise. | cond-mat_dis-nn |
On the Nature of Localization in Ti doped Si: Intermediate band semiconductors hold the promise to significantly improve
the efficiency of solar cells, but only if the intermediate impurity band is
metallic. We apply a recently developed first principles method to investigate
the origin of electron localization in Ti doped Si, a promising candidate for
intermediate band solar cells. Although Anderson localization is often
overlooked in the context of intermediate band solar cells, our results show
that in Ti doped Si it plays a more important role in the metal insulator
transition than Mott localization. Implications for the theory of intermediate
band solar cells are discussed. | cond-mat_dis-nn |
Inner Structure of Many-Body Localization Transition and Fulfillment of
Harris Criterion: We treat disordered Heisenberg model in 1D as the "standard model" of
many-body localization (MBL). Two independent order parameters stemming purely
from the half-chain von Neumann entanglement entropy $S_{\textrm{vN}}$ are
introduced to probe its eigenstate transition. From symmetry-endowed entropy
decomposition, they are probability distribution deviation $|d(p_n)|$ and von
Neumann entropy $S_{\textrm{vN}}^{n}(D_n\!=\!\mbox{max})$ of the
maximum-dimensional symmetry subdivision. Finite-size analyses reveal that
$\{p_n\}$ drives the localization transition, preceded by a thermalization
breakdown transition governed by $\{S_{\textrm{vN}}^{n}\}$. For noninteracting
case, these transitions coincide, but in interacting situation they separate.
Such separability creates an intermediate phase region and may help
discriminate between the Anderson and MBL transitions. An obstacle whose
solution eludes community to date is the violation of Harris criterion in
nearly all numeric investigations of MBL so far. Upon elucidating the mutually
independent components in $S_{\textrm{vN}}$, it is clear that previous studies
of eigenspectra, $S_{\textrm{vN}}$, and the like lack resolution to pinpoint
(thus completely overlook) the crucial internal structures of the transition.
We show, for the first time, that after this necessary decoupling, the
universal critical exponents for both transitions of $|d(p_n)|$ and
$S_{\textrm{vN}}^{n}(D_n\!=\!\mbox{max})$ fulfill the Harris criterion:
$\nu\approx2.0\ (\nu\approx1.5)$ for quench (quasirandom) disorder. Our work
puts forth "symmetry combined with entanglement" as the missing organization
principle for the generic eigenstate matter and transition. | cond-mat_dis-nn |
Generalized multifractality at the spin quantum Hall transition:
Percolation mapping and pure-scaling observables: This work extends the analysis of the generalized multifractality of critical
eigenstates at the spin quantum Hall transition in two-dimensional disordered
superconductors [J. F. Karcher et al, Annals of Physics, 435, 168584 (2021)]. A
mapping to classical percolation is developed for a certain set of
generalized-multifractality observables. In this way, exact analytical results
for the corresponding exponents are obtained. Furthermore, a general
construction of positive pure-scaling eigenfunction observables is presented,
which permits a very efficient numerical determination of scaling exponents. In
particular, all exponents corresponding to polynomial pure-scaling observables
up to the order $q=5$ are found numerically. For the observables for which the
percolation mapping is derived, analytical and numerical results are in perfect
agreement with each other. The analytical and numerical results unambiguously
demonstrate that the generalized parabolicity (i.e., proportionality to
eigenvalues of the quadratic Casimir operator) does not hold for the spectrum
of generalized-multifractality exponents. This excludes
Wess-Zumino-Novikov-Witten models, and, more generally, any theories with local
conformal invariance, as candidates for the fixed-point theory of the spin
quantum Hall transition. The observable construction developed in this work
paves a way to investigation of generalized multifractality at
Anderson-localization critical points of various symmetry classes. | cond-mat_dis-nn |
Random Dirac Fermions and Non-Hermitian Quantum Mechanics: We study the influence of a strong imaginary vector potential on the quantum
mechanics of particles confined to a two-dimensional plane and propagating in a
random impurity potential. We show that the wavefunctions of the non-Hermitian
operator can be obtained as the solution to a two-dimensional Dirac equation in
the presence of a random gauge field. Consequences for the localization
properties and the critical nature of the states are discussed. | cond-mat_dis-nn |
Effect of coupling asymmetry on mean-field solutions of direct and
inverse Sherrington-Kirkpatrick model: We study how the degree of symmetry in the couplings influences the
performance of three mean field methods used for solving the direct and inverse
problems for generalized Sherrington-Kirkpatrick models. In this context, the
direct problem is predicting the potentially time-varying magnetizations. The
three theories include the first and second order Plefka expansions, referred
to as naive mean field (nMF) and TAP, respectively, and a mean field theory
which is exact for fully asymmetric couplings. We call the last of these simply
MF theory. We show that for the direct problem, nMF performs worse than the
other two approximations, TAP outperforms MF when the coupling matrix is nearly
symmetric, while MF works better when it is strongly asymmetric. For the
inverse problem, MF performs better than both TAP and nMF, although an ad hoc
adjustment of TAP can make it comparable to MF. For high temperatures the
performance of TAP and MF approach each other. | cond-mat_dis-nn |
Flat band states: disorder and nonlinearity: We study the critical behaviour of Anderson localized modes near intersecting
flat and dispersive bands in the quasi-one-dimensional diamond ladder with weak
diagonal disorder $W$. The localization length $\xi$ of the flat band states
scales with disorder as $\xi \sim W^{-\gamma}$, with $\gamma \approx 1.3$, in
contrast to the dispersive bands with $\gamma =2$. A small fraction of
dispersive modes mixed with the flat band states is responsible for the unusual
scaling. Anderson localization is therefore controlled by two different length
scales. Nonlinearity can produce qualitatively different wave spreading
regimes, from enhanced expansion to resonant tunneling and self-trapping. | cond-mat_dis-nn |
Transition from localized to mean field behaviour of cascading failures
in the fiber bundle model on complex networks: We study the failure process of fiber bundles on complex networks focusing on
the effect of the degree of disorder of fibers' strength on the transition from
localized to mean field behaviour. Starting from a regular square lattice we
apply the Watts-Strogatz rewiring technique to introduce long range random
connections in the load transmission network and analyze how the ultimate
strength of the bundle and the statistics of the size of failure cascades
change when the rewiring probability is gradually increased. Our calculations
revealed that the degree of strength disorder of nodes of the network has a
substantial effect on the localized to mean field transition. In particular, we
show that the transition sets on at a finite value of the rewiring probability,
which shifts to higher values as the degree of disorder is reduced. The
transition is limited to a well defined range of disorder, so that there exists
a threshold disorder of nodes' strength below which the randomization of the
network structure does not provide any improvement neither of the overall load
bearing capacity nor of the cascade tolerance of the system. At low strength
disorder the fully random network is the most stable one, while at high
disorder best cascade tolerance is obtained at a lower structural randomness.
Based on the interplay of the network structure and strength disorder we
construct an analytical argument which provides a reasonable description of the
numerical findings. | cond-mat_dis-nn |
Anderson Localization on the Bethe Lattice using Cages and the Wegner
Flow: Anderson localization on tree-like graphs such as the Bethe lattice, Cayley
tree, or random regular graphs has attracted attention due to its apparent
mathematical tractability, hypothesized connections to many-body localization,
and the possibility of non-ergodic extended regimes. This behavior has been
conjectured to also appear in many-body localization as a "bad metal" phase,
and constitutes an intermediate possibility between the extremes of ergodic
quantum chaos and integrable localization. Despite decades of research, a
complete consensus understanding of this model remains elusive. Here, we use
cages, maximally tree-like structures from extremal graph theory; and numerical
continuous unitary Wegner flows of the Anderson Hamiltonian to develop an
intuitive picture which, after extrapolating to the infinite Bethe lattice,
appears to capture ergodic, non-ergodic extended, and fully localized behavior. | cond-mat_dis-nn |
Spurious self-feedback of mean-field predictions inflates infection
curves: The susceptible-infected-recovered (SIR) model and its variants form the
foundation of our understanding of the spread of diseases. Here, each agent can
be in one of three states (susceptible, infected, or recovered), and
transitions between these states follow a stochastic process. The probability
of an agent becoming infected depends on the number of its infected neighbors,
hence all agents are correlated. A common mean-field theory of the same
stochastic process however, assumes that the agents are statistically
independent. This leads to a self-feedback effect in the approximation: when an
agent infects its neighbors, this infection may subsequently travel back to the
original agent at a later time, leading to a self-infection of the agent which
is not present in the underlying stochastic process. We here compute the first
order correction to the mean-field assumption, which takes fluctuations up to
second order in the interaction strength into account. We find that it cancels
the self-feedback effect, leading to smaller infection rates. In the SIR model
and in the SIRS model, the correction significantly improves predictions. In
particular, it captures how sparsity dampens the spread of the disease: this
indicates that reducing the number of contacts is more effective than predicted
by mean-field models. | cond-mat_dis-nn |
Critical synchronization dynamics of the Kuramoto model on connectome
and small world graphs: The hypothesis, that cortical dynamics operates near criticality also
suggests, that it exhibits universal critical exponents which marks the
Kuramoto equation, a fundamental model for synchronization, as a prime
candidate for an underlying universal model. Here, we determined the
synchronization behavior of this model by solving it numerically on a large,
weighted human connectome network, containing 804092 nodes, in an assumed
homeostatic state. Since this graph has a topological dimension $d < 4$, a real
synchronization phase transition is not possible in the thermodynamic limit,
still we could locate a transition between partially synchronized and
desynchronized states. At this crossover point we observe power-law--tailed
synchronization durations, with $\tau_t \simeq 1.2(1)$, away from experimental
values for the brain. For comparison, on a large two-dimensional lattice,
having additional random, long-range links, we obtain a mean-field value:
$\tau_t \simeq 1.6(1)$. However, below the transition of the connectome we
found global coupling control-parameter dependent exponents $1 < \tau_t \le 2$,
overlapping with the range of human brain experiments. We also studied the
effects of random flipping of a small portion of link weights, mimicking a
network with inhibitory interactions, and found similar results. The
control-parameter dependent exponent suggests extended dynamical criticality
below the transition point. | cond-mat_dis-nn |
Critical Percolation Without Fine Tuning on the Surface of a Topological
Superconductor: We present numerical evidence that most two-dimensional surface states of a
bulk topological superconductor (TSC) sit at an integer quantum Hall plateau
transition. We study TSC surface states in class CI with quenched disorder.
Low-energy (finite-energy) surface states were expected to be critically
delocalized (Anderson localized). We confirm the low-energy picture, but find
instead that finite-energy states are also delocalized, with universal
statistics that are independent of the TSC winding number, and consistent with
the spin quantum Hall plateau transition (percolation). | cond-mat_dis-nn |
The number of matchings in random graphs: We study matchings on sparse random graphs by means of the cavity method. We
first show how the method reproduces several known results about maximum and
perfect matchings in regular and Erdos-Renyi random graphs. Our main new result
is the computation of the entropy, i.e. the leading order of the logarithm of
the number of solutions, of matchings with a given size. We derive both an
algorithm to compute this entropy for an arbitrary graph with a girth that
diverges in the large size limit, and an analytic result for the entropy in
regular and Erdos-Renyi random graph ensembles. | cond-mat_dis-nn |
Non-trivial fixed point structure of the two-dimensional +-J 3-state
Potts ferromagnet/spin glass: The fixed point structure of the 2D 3-state random-bond Potts model with a
bimodal ($\pm$J) distribution of couplings is for the first time fully
determined using numerical renormalization group techniques. Apart from the
pure and T=0 critical fixed points, two other non-trivial fixed points are
found. One is the critical fixed point for the random-bond, but unfrustrated,
ferromagnet. The other is a bicritical fixed point analogous to the bicritical
Nishimori fixed point found in the random-bond frustrated Ising model.
Estimates of the associated critical exponents are given for the various fixed
points of the random-bond Potts model. | cond-mat_dis-nn |
Retrieval and Chaos in Extremely Diluted Non-Monotonic Neural Networks: We discuss, in this paper, the dynamical properties of extremely diluted,
non-monotonic neural networks. Assuming parallel updating and the Hebb
prescription for the synaptic connections, a flow equation for the macroscopic
overlap is derived. A rich dynamical phase diagram was obtained, showing a
stable retrieval phase, as well as a cycle two and chaotic behavior. Numerical
simulations were performed, showing good agreement with analytical results.
Furthermore, the simulations give an additional insight into the microscopic
dynamical behavior during the chaotic phase. It is shown that the freezing of
individual neuron states is related to the structure of chaotic attractors. | cond-mat_dis-nn |
Spin glass induced by infinitesimal disorder in geometrically frustrated
kagome lattice: We propose a method to study the magnetic properties of a disordered Ising
kagome lattice. The model considers small spin clusters with infinite-range
disordered couplings and short-range ferromagnetic (FE) or antiferromagnetic
interactions. The correlated cluster mean-field theory is used to obtain an
effective single-cluster problem. A finite disorder intensity in FE kagome
lattice introduces a cluster spin-glass (CSG) phase. Nevertheless, an
infinitesimal disorder stabilizes the CSG behavior in the geometrically
frustrated kagome system. Entropy, magnetic susceptibility and spin-spin
correlation are used to describe the interplay between disorder and geometric
frustration (GF). We find that GF plays an important role in the low-disorder
CSG phase. However, the increase of disorder can rule out the effect of GF. | cond-mat_dis-nn |
Wave Transport in disordered waveguides: closed channel contributions
and the coherent and diffuse fields: We study the wave transport through a disordered system inside a waveguide.
The expectation value of the complex reflection and transmission coefficients
(the coherent fields) as well as the transmittance and reflectance are obtained
numerically. The numerical results show that the averages of the coherent
fields are only relevant for direct processes, while the transmittance and
reflectance are mainly dominated by the diffuse intensities, which come from
the statistical fluctuations of the fields. | cond-mat_dis-nn |
How to predict critical state: Invariance of Lyapunov exponent in dual
spaces: The critical state in disordered systems, a fascinating and subtle
eigenstate, has attracted a lot of research interest. However, the nature of
the critical state is difficult to describe quantitatively. Most of the studies
focus on numerical verification, and cannot predict the system in which the
critical state exists. In this work, we propose an explicit and universal
criterion that for the critical state Lyapunov exponent should be 0
simultaneously in dual spaces, namely Lyapunov exponent remains invariant under
Fourier transform. With this criterion, we exactly predict a specific system
hosting a large number of critical states for the first time. Then, we perform
numerical verification of the theoretical prediction, and display the
self-similarity and scale invariance of the critical state. Finally, we
conjecture that there exist some kind of connection between the invariance of
the Lyapunov exponent and conformal invariance. | cond-mat_dis-nn |
Stability of networks of delay-coupled delay oscillators: Dynamical networks with time delays can pose a considerable challenge for
mathematical analysis. Here, we extend the approach of generalized modeling to
investigate the stability of large networks of delay-coupled delay oscillators.
When the local dynamical stability of the network is plotted as a function of
the two delays then a pattern of tongues is revealed. Exploiting a link between
structure and dynamics, we identify conditions under which perturbations of the
topology have a strong impact on the stability. If these critical regions are
avoided the local stability of large random networks can be well approximated
analytically. | cond-mat_dis-nn |
Evidence for the double degeneracy of the ground-state in the 3D $\pm J$
spin glass: A bivariate version of the multicanonical Monte Carlo method and its
application to the simulation of the three-dimensional $\pm J$ Ising spin glass
are described. We found the autocorrelation time associated with this
particular multicanonical method was approximately proportional to the system
volume, which is a great improvement over previous methods applied to
spin-glass simulations. The principal advantage of this version of the
multicanonical method, however, was its ability to access information
predictive of low-temperature behavior. At low temperatures we found results on
the three-dimensional $\pm J$ Ising spin glass consistent with a double
degeneracy of the ground-state: the order-parameter distribution function
$P(q)$ converged to two delta-function peaks and the Binder parameter
approached unity as the system size was increased. With the same density of
states used to compute these properties at low temperature, we found their
behavior changing as the temperature is increased towards the spin glass
transition temperature. Just below this temperature, the behavior is consistent
with the standard mean-field picture that has an infinitely degenerate ground
state. Using the concept of zero-energy droplets, we also discuss the structure
of the ground-state degeneracy. The size distribution of the zero-energy
droplets was found to produce the two delta-function peaks of $P(q)$. | cond-mat_dis-nn |
Comment on "Collective modes and gapped momentum states in liquid Ga:
Experiment, theory, and simulation": We show that the presented in Phys.Rev.B, v.101, 214312 (2020) theoretical
expressions for longitudinal current spectral function $C^L(k,\omega)$ and
dispersion of collective excitations are not correct. Indeed, they are not
compatible with the continuum limit and $C^L(k,\omega\to 0)$ contradicts the
continuity equation. | cond-mat_dis-nn |
Finite-time Singularities in Surface-Diffusion Instabilities are Cured
by Plasticity: A free material surface which supports surface diffusion becomes unstable
when put under external non-hydrostatic stress. Since the chemical potential on
a stressed surface is larger inside an indentation, small shape fluctuations
develop because material preferentially diffuses out of indentations. When the
bulk of the material is purely elastic one expects this instability to run into
a finite-time cusp singularity. It is shown here that this singularity is cured
by plastic effects in the material, turning the singular solution to a regular
crack. | cond-mat_dis-nn |
Transport of multiple users in complex networks: We study the transport properties of model networks such as scale-free and
Erd\H{o}s-R\'{e}nyi networks as well as a real network. We consider the
conductance $G$ between two arbitrarily chosen nodes where each link has the
same unit resistance. Our theoretical analysis for scale-free networks predicts
a broad range of values of $G$, with a power-law tail distribution $\Phi_{\rm
SF}(G)\sim G^{-g_G}$, where $g_G=2\lambda -1$, and $\lambda$ is the decay
exponent for the scale-free network degree distribution. We confirm our
predictions by large scale simulations. The power-law tail in $\Phi_{\rm
SF}(G)$ leads to large values of $G$, thereby significantly improving the
transport in scale-free networks, compared to Erd\H{o}s-R\'{e}nyi networks
where the tail of the conductivity distribution decays exponentially. We
develop a simple physical picture of the transport to account for the results.
We study another model for transport, the \emph{max-flow} model, where
conductance is defined as the number of link-independent paths between the two
nodes, and find that a similar picture holds. The effects of distance on the
value of conductance are considered for both models, and some differences
emerge. We then extend our study to the case of multiple sources, where the
transport is define between two \emph{groups} of nodes. We find a fundamental
difference between the two forms of flow when considering the quality of the
transport with respect to the number of sources, and find an optimal number of
sources, or users, for the max-flow case. A qualitative (and partially
quantitative) explanation is also given. | cond-mat_dis-nn |
Stability of critical behaviour of weakly disordered systems with
respect to the replica symmetry breaking: A field-theoretic description of the critical behaviour of the weakly
disordered systems is given. Directly, for three- and two-dimensional systems a
renormalization analysis of the effective Hamiltonian of model with replica
symmetry breaking (RSB) potentials is carried out in the two-loop
approximation. For case with 1-step RSB the fixed points (FP's) corresponding
to stability of the various types of critical behaviour are identified with the
use of the Pade-Borel summation technique. Analysis of FP's has shown a
stability of the critical behaviour of the weakly disordered systems with
respect to RSB effects and realization of former scenario of disorder influence
on critical behaviour. | cond-mat_dis-nn |
Phase transitions induced by microscopic disorder: a study based on the
order parameter expansion: Based on the order parameter expansion, we present an approximate method
which allows us to reduce large systems of coupled differential equations with
diverse parameters to three equations: one for the global, mean field, variable
and two which describe the fluctuations around this mean value. With this tool
we analyze phase-transitions induced by microscopic disorder in three
prototypical models of phase-transitions which have been studied previously in
the presence of thermal noise. We study how macroscopic order is induced or
destroyed by time independent local disorder and analyze the limits of the
approximation by comparing the results with the numerical solutions of the
self-consistency equation which arises from the property of self-averaging.
Finally, we carry on a finite-size analysis of the numerical results and
calculate the corresponding critical exponents. | cond-mat_dis-nn |
Observation of infinite-range intensity correlations above, at and below
the 3D Anderson localization transition: We investigate long-range intensity correlations on both sides of the
Anderson transition of classical waves in a three-dimensional (3D) disordered
material. Our ultrasonic experiments are designed to unambiguously detect a
recently predicted infinite-range C0 contribution, due to local density of
states fluctuations near the source. We find that these C0 correlations, in
addition to C2 and C3 contributions, are significantly enhanced near mobility
edges. Separate measurements of the inverse participation ratio reveal a link
between C0 and the anomalous dimension \Delta_2, implying that C0 may also be
used to explore the critical regime of the Anderson transition. | cond-mat_dis-nn |
Challenges and opportunities in the supervised learning of quantum
circuit outputs: Recently, deep neural networks have proven capable of predicting some output
properties of relevant random quantum circuits, indicating a strategy to
emulate quantum computers alternative to direct simulation methods such as,
e.g., tensor-network methods. However, the reach of this alternative strategy
is not yet clear. Here we investigate if and to what extent neural networks can
learn to predict the output expectation values of circuits often employed in
variational quantum algorithms, namely, circuits formed by layers of CNOT gates
alternated with random single-qubit rotations. On the one hand, we find that
the computational cost of supervised learning scales exponentially with the
inter-layer variance of the random angles. This allows entering a regime where
quantum computers can easily outperform classical neural networks. On the other
hand, circuits featuring only inter-qubit angle variations are easily emulated.
In fact, thanks to a suitable scalable design, neural networks accurately
predict the output of larger and deeper circuits than those used for training,
even reaching circuit sizes which turn out to be intractable for the most
common simulation libraries, considering both state-vector and tensor-network
algorithms. We provide a repository of testing data in this regime, to be used
for future benchmarking of quantum devices and novel classical algorithms. | cond-mat_dis-nn |
Stability of a neural network model with small-world connections: Small-world networks are highly clustered networks with small distances among
the nodes. There are many biological neural networks that present this kind of
connections. There are no special weightings in the connections of most
existing small-world network models. However, this kind of simply-connected
models cannot characterize biological neural networks, in which there are
different weights in synaptic connections. In this paper, we present a neural
network model with weighted small-world connections, and further investigate
the stability of this model. | cond-mat_dis-nn |
Numerical Simulations of Random Phase Sine-Gordon Model and
Renormalization Group Predictions: Numerical Simulations of the random phase sine-Gordon model suffer from
strong finite size effects preventing the non-Gaussian $\log^2 r$ component of
the spatial correlator from following the universal infinite volume prediction.
We show that a finite size prediction based on perturbative Renormalisation
Group (RG) arguments agrees well with new high precision simulations for small
coupling and close to the critical temperature. | cond-mat_dis-nn |
Localization properties of the sparse Barrat-Mézard trap model: Inspired by works on the Anderson model on sparse graphs, we devise a method
to analyze the localization properties of sparse systems that may be solved
using cavity theory. We apply this method to study the properties of the
eigenvectors of the master operator of the sparse Barrat-M\'ezard trap model,
with an emphasis on the extended phase. As probes for localization, we consider
the inverse participation ratio and the correlation volume, both dependent on
the distribution of the diagonal elements of the resolvent. Our results reveal
a rich and non-trivial behavior of the estimators across the spectrum of
relaxation rates and an interplay between entropic and activation mechanisms of
relaxation that give rise to localized modes embedded in the bulk of extended
states. We characterize this route to localization and find it to be distinct
from the paradigmatic Anderson model or standard random matrix systems. | cond-mat_dis-nn |
A dedicated algorithm for calculating ground states for the triangular
random bond Ising model: In the presented article we present an algorithm for the computation of
ground state spin configurations for the 2d random bond Ising model on planar
triangular lattice graphs. Therefore, it is explained how the respective ground
state problem can be mapped to an auxiliary minimum-weight perfect matching
problem, solvable in polynomial time. Consequently, the ground state properties
as well as minimum-energy domain wall (MEDW) excitations for very large 2d
systems, e.g. lattice graphs with up to N=384x384 spins, can be analyzed very
fast. Here, we investigate the critical behavior of the corresponding T=0
ferromagnet to spin-glass transition, signaled by a breakdown of the
magnetization, using finite-size scaling analyses of the magnetization and MEDW
excitation energy and we contrast our numerical results with previous
simulations and presumably exact results. | cond-mat_dis-nn |
Distribution of shortest cycle lengths in random networks: We present analytical results for the distribution of shortest cycle lengths
(DSCL) in random networks. The approach is based on the relation between the
DSCL and the distribution of shortest path lengths (DSPL). We apply this
approach to configuration model networks, for which analytical results for the
DSPL were obtained before. We first calculate the fraction of nodes in the
network which reside on at least one cycle. Conditioning on being on a cycle,
we provide the DSCL over ensembles of configuration model networks with degree
distributions which follow a Poisson distribution (Erdos-R\'enyi network),
degenerate distribution (random regular graph) and a power-law distribution
(scale-free network). The mean and variance of the DSCL are calculated. The
analytical results are found to be in very good agreement with the results of
computer simulations. | cond-mat_dis-nn |
Low Temperature Behavior of the Thermopower in Disordered Systems near
the Anderson Transition: We investigate the behavior of the thermoelectric power [S] in disordered
systems close to the Anderson-type metal-insulator transition [MIT] at low
temperatures. In the literature, we find contradictory results for S. It is
either argued to diverge or to remain a constant as the MIT is approached. To
resolve this dilemma, we calculate the number density of electrons at the MIT
in disordered systems using an averaged density of states obtained by
diagonalizing the three-dimensional Anderson model of localization. From the
number density we obtain the temperature dependence of the chemical potential
necessary to solve for S. Without any additional approximation, we use the
Chester-Thellung-Kubo-Greenwood formulation and numerically obtain the behavior
of S at low T as the Anderson transition is approached from the metallic side.
We show that indeed S does not diverge. | cond-mat_dis-nn |
Chemical potential in disordered organic materials: Charge carrier mobility in disordered organic materials is being actively
studied, motivated by several applications such as organic light emitting
diodes and organic field-effect transistors. It is known that the mobility in
disordered organic materials depends on the chemical potential which in turn
depends on the carrier concentration. However, the functional dependence of
chemical potential on the carrier concentration is not known. In this study, we
focus on the chemical potential in organic materials with Gaussian disorder. We
identify three cases of non-degenerate, degenerate and saturated regimes. In
each regime we calculate analytically the chemical potential as a function of
the carrier concentration and the energetic disorder from the first principles. | cond-mat_dis-nn |
The perturbative structure of spin glass field theory: Cubic replicated field theory is used to study the glassy phase of the
short-range Ising spin glass just below the transition temperature, and for
systems above, at, and slightly below the upper critical dimension six. The
order parameter function is computed up to two-loop order. There are two,
well-separated bands in the mass spectrum, just as in mean field theory. The
small mass band acts as an infrared cutoff, whereas contributions from the
large mass region can be computed perturbatively (d>6), or interpreted by the
epsilon-expansion around the critical fixed point (d=6-epsilon). The one-loop
calculation of the (momentum-dependent) longitudinal mass, and the whole
replicon sector is also presented. The innocuous behavior of the replicon
masses while crossing the upper critical dimension shows that the ultrametric
replica symmetry broken phase remains stable below six dimensions. | cond-mat_dis-nn |
A FDR-preserving field theory for interacting Brownian particles:
one-loop theory and MCT: We develop a field theoretical treatment of a model of interacting Brownian
particles. We pay particular attention to the requirement of the time reversal
invariance and the fluctuation-dissipation relationship (FDR). The method used
is a modified version of the auxiliary field method due originally to
Andreanov, Biroli and Lefevre [J. Stat. Mech. P07008 (2006)]. We recover the
correct diffusion law when the interaction is dropped as well as the standard
mode coupling equation in the one-loop order calculation for interacting
Brownian particle systems. | cond-mat_dis-nn |
On calculation of effective conductivity of inhomogeneous metals: In the framework of the perturbation theory an expression suitable for
calculation of the effective conductivity of 3-D inhomogeneous metals is
derived. Formally, the final expression is an exact result, however, a function
written as a perturbation series enters the answer. More accurately, when
statistical properties of the given inhomogeneous medium are known, our result
provides the regular algorithm for calculation of the effective conductivity up
to an arbitrary term of the perturbation series. As examples, we examine (i) an
isotropic metal whose local conductivity is a Gaussianly distributed random
function, (ii) the effective conductivity of polycrystalline metals. | cond-mat_dis-nn |
Comment on "Failure of the simultaneous block diagonalization technique
applied to complete and cluster synchronization of random networks": In their recent preprint [arXiv:2108.07893v1], S. Panahi, N. Amaya, I.
Klickstein, G. Novello, and F. Sorrentino tested the simultaneous block
diagonalization (SBD) technique on synchronization in random networks and found
the dimensionality reduction to be limited. Based on this observation, they
claimed the SBD technique to be a failure in generic situations. Here, we show
that this is not a failure of the SBD technique. Rather, it is caused by
inappropriate choices of network models. SBD provides a unified framework to
analyze the stability of synchronization patterns that are not encumbered by
symmetry considerations, and it always finds the optimal reduction for any
given synchronization pattern and network structure [SIAM Rev. 62, 817-836
(2020)]. The networks considered by Panahi et al. are poor benchmarks for the
performance of the SBD technique, as these systems are often intrinsically
irreducible, regardless of the method used. Thus, although the results in
Panahi et al. are technically valid, their interpretations are misleading and
akin to claiming a community detection algorithm to be a failure because it
does not find any meaningful communities in Erd\H{o}s-R\'enyi networks. | cond-mat_dis-nn |
Molecular dynamics simulation of aging in amorphous silica: By means of molecular dynamics simulations we examine the aging process of a
strong glass former, a silica melt modeled by the BKS potential. The system is
quenched from a temperature above to one below the critical temperature, and
the potential energy and the scattering function C(t_w,t+t_w) for various
waiting times t_w after the quench are measured. We find that both
qualitatively and quantitatively the results agree well with the ones found in
similar simulations of a fragile glass former, a Lennard-Jones liquid. | cond-mat_dis-nn |
Critical dynamics on a large human Open Connectome network: Extended numerical simulations of threshold models have been performed on a
human brain network with N=836733 connected nodes available from the Open
Connectome project. While in case of simple threshold models a sharp
discontinuous phase transition without any critical dynamics arises, variable
thresholds models exhibit extended power-law scaling regions. This is
attributed to fact that Griffiths effects, stemming from the
topological/interaction heterogeneity of the network, can become relevant if
the input sensitivity of nodes is equalized. I have studied the effects effects
of link directness, as well as the consequence of inhibitory connections.
Non-universal power-law avalanche size and time distributions have been found
with exponents agreeing with the values obtained in electrode experiments of
the human brain. The dynamical critical region occurs in an extended control
parameter space without the assumption of self organized criticality. | cond-mat_dis-nn |
Classical Representation of the 1D Anderson Model: A new approach is applied to the 1D Anderson model by making use of a
two-dimensional Hamiltonian map. For a weak disorder this approach allows for a
simple derivation of correct expressions for the localization length both at
the center and at the edge of the energy band, where standard perturbation
theory fails. Approximate analytical expressions for strong disorder are also
obtained. | cond-mat_dis-nn |
Comment on "Critical point scaling of Ising spin glasses in a magnetic
field" by J. Yeo and M.A. Moore: In a section of a recent publication, [J. Yeo and M.A. Moore, Phys. Rev. B
91, 104432 (2015)], the authors discuss some of the arguments in the paper by
Parisi and Temesv\'ari [Nuclear Physics B 858, 293 (2012)]. In this comment, it
is shown how these arguments are misinterpreted, and the existence of the
Almeida-Thouless transition in the upper critical dimension 6 reasserted. | cond-mat_dis-nn |
The Anderson transition: time reversal symmetry and universality: We report a finite size scaling study of the Anderson transition. Different
scaling functions and different values for the critical exponent have been
found, consistent with the existence of the orthogonal and unitary universality
classes which occur in the field theory description of the transition. The
critical conductance distribution at the Anderson transition has also been
investigated and different distributions for the orthogonal and unitary classes
obtained. | cond-mat_dis-nn |
Pure scaling operators at the integer quantum Hall plateau transition: Stationary wave functions at the transition between plateaus of the integer
quantum Hall effect are known to exhibit multi-fractal statistics. Here we
explore this critical behavior for the case of scattering states of the
Chalker-Coddington model with point contacts. We argue that moments formed from
the wave amplitudes of critical scattering states decay as pure powers of the
distance between the points of contact and observation. These moments in the
continuum limit are proposed to be correlations functions of primary fields of
an underlying conformal field theory. We check this proposal numerically by
finite-size scaling. We also verify the CFT prediction for a 3-point function
involving two primary fields. | cond-mat_dis-nn |
Field theory for amorphous solids: Glasses at low temperature fluctuate around their inherent states; glassy
anomalies reflect the structure of these states. Recently there have been
numerous observations of long-range stress correlations in glassy materials,
from supercooled liquids to colloids and granular materials, but without a
common explanation. Herein it is shown, using a field theory of inherent
states, that long-range stress correlations follow from mechanical equilibrium
alone, with explicit predictions for stress correlations in 2 and 3 dimensions.
`Equations of state' relating fluctuations to imposed stresses are derived, as
well as field equations that fix the spatial structure of stresses in arbitrary
geometries. Finally, a new holographic quantity in 3D amorphous systems is
identified. | cond-mat_dis-nn |
Metallic phase of disordered graphene superlattices with long-range
correlations: Using the transfer matrix method, we study the conductance of the chiral
particles through a monolayer graphene superlattice with long-range correlated
disorder distributed on the potential of the barriers. Even though the
transmission of the particles through graphene superlattice with white noise
potentials is suppressed, the transmission is revived in a wide range of angles
when the potential heights are long-range correlated with a power spectrum
$S(k)\sim1/k^{\beta}$. As a result, the conductance increases with increasing
the correlation exponent values gives rise a metallic phase. We obtain a phase
transition diagram in which a critical correlation exponent depends strongly on
disorder strength and slightly on the energy of the incident particles. The
phase transition, on the other hand, appears in all ranges of the energy from
propagating to evanescent mode regimes. | cond-mat_dis-nn |
Well-mixed Lotka-Volterra model with random strongly competitive
interactions: The random Lotka-Volterra model is widely used to describe the dynamical and
thermodynamic features of ecological communities. In this work, we consider
random symmetric interactions between species and analyze the strongly
competitive interaction case. We investigate different scalings for the
distribution of the interactions with the number of species and try to bridge
the gap with previous works. Our results show two different behaviors for the
mean abundance at zero and finite temperature respectively, with a continuous
crossover between the two. We confirm and extend previous results obtained for
weak interactions: at zero temperature, even in the strong competitive
interaction limit, the system is in a multiple-equilibria phase, whereas at
finite temperature only a unique stable equilibrium can exist. Finally, we
establish the qualitative phase diagrams in both cases and compare the two
species abundance distributions. | cond-mat_dis-nn |
Critical parameters for the disorder-induced metal-insulator transition
in FCC and BCC lattices: We use a transfer-matrix method to study the disorder-induced metal-insulator
transition. We take isotropic nearest- neighbor hopping and an onsite potential
with uniformly distributed disorder. Following previous work done on the simple
cubic lattice, we perform numerical calculations for the body centered cubic
and face centered cubic lattices, which are more common in nature. We obtain
the localization length from calculated Lyapunov exponents for different system
sizes. This data is analyzed using finite-size scaling to find the critical
parameters. We create an energy-disorder phase diagram for both lattice types,
noting that it is symmetric about the band center for the body centered cubic
lattice, but not for the face centered cubic lattice. We find a critical
exponent of approximately 1.5-1.6 for both lattice types for transitions
occurring either at fixed energy or at fixed disorder, agreeing with results
previously obtained for other systems belonging to the same orthogonal
universality class. We notice an increase in critical disorder with the number
of nearest neighbors, which agrees with intuition. | cond-mat_dis-nn |
Optimal fluctuation approach to a directed polymer in a random medium: A modification of the optimal fluctuation approach is applied to study the
tails of the free energy distribution function P(F) for an elastic string in
quenched disorder both in the regions of the universal behavior of P(F) and in
the regions of large fluctuations, where the behavior of P(F) is non-universal.
The difference between the two regimes is shown to consist in whether it is
necessary or not to take into account the renormalization of parameters by the
fluctuations of disorder in the vicinity of the optimal fluctuation. | cond-mat_dis-nn |
Critical parameters for the disorder-induced metal-insulator transition
in FCC and BCC lattices: We use a transfer-matrix method to study the disorder-induced metal-insulator
transition. We take isotropic nearest- neighbor hopping and an onsite potential
with uniformly distributed disorder. Following previous work done on the simple
cubic lattice, we perform numerical calculations for the body centered cubic
and face centered cubic lattices, which are more common in nature. We obtain
the localization length from calculated Lyapunov exponents for different system
sizes. This data is analyzed using finite-size scaling to find the critical
parameters. We create an energy-disorder phase diagram for both lattice types,
noting that it is symmetric about the band center for the body centered cubic
lattice, but not for the face centered cubic lattice. We find a critical
exponent of approximately 1.5-1.6 for both lattice types for transitions
occurring either at fixed energy or at fixed disorder, agreeing with results
previously obtained for other systems belonging to the same orthogonal
universality class. We notice an increase in critical disorder with the number
of nearest neighbors, which agrees with intuition. | cond-mat_dis-nn |
Percolation theory applied to measures of fragmentation in social
networks: We apply percolation theory to a recently proposed measure of fragmentation
$F$ for social networks. The measure $F$ is defined as the ratio between the
number of pairs of nodes that are not connected in the fragmented network after
removing a fraction $q$ of nodes and the total number of pairs in the original
fully connected network. We compare $F$ with the traditional measure used in
percolation theory, $P_{\infty}$, the fraction of nodes in the largest cluster
relative to the total number of nodes. Using both analytical and numerical
methods from percolation, we study Erd\H{o}s-R\'{e}nyi (ER) and scale-free (SF)
networks under various types of node removal strategies. The removal strategies
are: random removal, high degree removal and high betweenness centrality
removal. We find that for a network obtained after removal (all strategies) of
a fraction $q$ of nodes above percolation threshold, $P_{\infty}\approx
(1-F)^{1/2}$. For fixed $P_{\infty}$ and close to percolation threshold
($q=q_c$), we show that $1-F$ better reflects the actual fragmentation. Close
to $q_c$, for a given $P_{\infty}$, $1-F$ has a broad distribution and it is
thus possible to improve the fragmentation of the network. We also study and
compare the fragmentation measure $F$ and the percolation measure $P_{\infty}$
for a real social network of workplaces linked by the households of the
employees and find similar results. | cond-mat_dis-nn |
Correlated Domains in Spin Glasses: We study the 3D Edwards-Anderson spin glasses, by analyzing spin-spin
correlation functions in thermalized spin configurations at low T on large
lattices. We consider individual disorder samples and analyze connected
clusters of very correlated sites: we analyze how the volume and the surface of
these clusters increases with the lattice size. We qualify the important
excitations of the system by checking how large they are, and we define a
correlation length by measuring their gyration radius. We find that the
clusters have a very dense interface, compatible with being space filling. | cond-mat_dis-nn |
Irreversible Opinion Spreading on Scale-Free Networks: We study the dynamical and critical behavior of a model for irreversible
opinion spreading on Barab\'asi-Albert (BA) scale-free networks by performing
extensive Monte Carlo simulations. The opinion spreading within an
inhomogeneous society is investigated by means of the magnetic Eden model, a
nonequilibrium kinetic model for the growth of binary mixtures in contact with
a thermal bath. The deposition dynamics, which is studied as a function of the
degree of the occupied sites, shows evidence for the leading role played by
hubs in the growth process. Systems of finite size grow either ordered or
disordered, depending on the temperature. By means of standard finite-size
scaling procedures, the effective order-disorder phase transitions are found to
persist in the thermodynamic limit. This critical behavior, however, is absent
in related equilibrium spin systems such as the Ising model on BA scale-free
networks, which in the thermodynamic limit only displays a ferromagnetic phase.
The dependence of these results on the degree exponent is also discussed for
the case of uncorrelated scale-free networks. | cond-mat_dis-nn |
Universal Sound Absorption in Amorphous Solids: A Theory of Elastically
Coupled Generic Blocks: Glasses are known to exhibit quantitative universalities at low temperatures,
the most striking of which is the ultrasonic attenuation coefficient 1/Q. In
this work we develop a theory of coupled generic blocks with a certain
randomness property to show that universality emerges essentially due to the
interactions between elastic blocks, regardless of their microscopic nature. | cond-mat_dis-nn |
Speeding protein folding beyond the Go model: How a little frustration
sometimes helps: Perturbing a Go model towards a realistic protein Hamiltonian by adding
non-native interactions, we find that the folding rate is in general enhanced
as ruggedness is initially increased, as long as the protein is sufficiently
large and flexible. Eventually the rate drops rapidly towards zero when
ruggedness significantly slows conformational transitions. Energy landscape
arguments for thermodynamics and kinetics are coupled with a treatment of
non-native collapse to elucidate this effect. | cond-mat_dis-nn |
Imaginary replica analysis of loopy regular random graphs: We present an analytical approach for describing spectrally constrained
maximum entropy ensembles of finitely connected regular loopy graphs, valid in
the regime of weak loop-loop interactions. We derive an expression for the
leading two orders of the expected eigenvalue spectrum, through the use of
infinitely many replica indices taking imaginary values. We apply the method to
models in which the spectral constraint reduces to a soft constraint on the
number of triangles, which exhibit `shattering' transitions to phases with
extensively many disconnected cliques, to models with controlled numbers of
triangles and squares, and to models where the spectral constraint reduces to a
count of the number of adjacency matrix eigenvalues in a given interval. Our
predictions are supported by MCMC simulations based on edge swaps with
nontrivial acceptance probabilities. | cond-mat_dis-nn |
Comparison of Gabay-Toulouse and de Almeida-Thouless instabilities for
the spin glass XY model in a field on sparse random graphs: Vector spin glasses are known to show two different kinds of phase
transitions in presence of an external field: the so-called de Almeida-Thouless
and Gabay-Toulouse lines. While the former has been studied to some extent on
several topologies (fully connected, random graphs, finite-dimensional
lattices, chains with long-range interactions), the latter has been studied
only in fully connected models, which however are known to show some unphysical
behaviors (e.g. the divergence of these critical lines in the zero-temperature
limit). Here we compute analytically both these critical lines for XY spin
glasses on random regular graphs. We discuss the different nature of these
phase transitions and the dependence of the critical behavior on the field
distribution. We also study the crossover between the two different critical
behaviors, by suitably tuning the field distribution. | cond-mat_dis-nn |
Distribution of the delay time and the dwell time for wave reflection
from a long random potential: We re-examine and correct an earlier derivation of the distribution of the
Wigner phase delay time for wave reflection from a long one-dimensional
disordered conductor treated in the continuum limit. We then numerically
compare the distributions of the Wigner phase delay time and the dwell time,
the latter being obtained by the use of an infinitesimal imaginary potential as
a clock, and investigate the effects of strong disorder and a periodic
(discrete) lattice background. We find that the two distributions coincide even
for strong disorder, but only for energies well away from the band-edges. | cond-mat_dis-nn |
Raman Scattering Due to Disorder-Induced Polaritons: The selection rules for dipole and Raman activity can be relaxed due to local
distortion of a crystalline structure. In this situation a dipole-inactive mode
can become simultaneously active in Raman scattering and in dipole interaction
with the electromagnetic field. The later interaction results in
disorder-induced polaritons, which could be observed in first-order Raman
spectra. We calculate scattering cross-section in the case of a material with a
diamond-like average structure, and show that there exist a strong possibility
of observing the disorder induced polaritons. | cond-mat_dis-nn |
Some Exact Results on the Ultrametric Overlap Distribution in Mean Field
Spin Glass Models (I): The mean field spin glass model is analyzed by a combination of
mathematically rigororous methods and a powerful Ansatz. The method exploited
is general, and can be applied to others disordered mean field models such as,
e.g., neural networks.
It is well known that the probability measure of overlaps among replicas
carries the whole physical content of these models. A functional order
parameter of Parisi type is introduced by rigorous methods, according to
previous works by F. Guerra. By the Ansatz that the functional order parameter
is the correct order parameter of the model, we explicitly find the full
overlap distribution. The physical interpretation of the functional order
parameter is obtained, and ultrametricity of overlaps is derived as a natural
consequence of a branching diffusion process.
It is shown by explicit construction that ultrametricity of the 3-replicas
overlap distribution together with the Ghirlanda-Guerra relations determines
the distribution of overlaps among s replicas, for any s, in terms of the
one-overlap distribution. | cond-mat_dis-nn |
Optimization by thermal cycling: Thermal cycling is an heuristic optimization algorithm which consists of
cyclically heating and quenching by Metropolis and local search procedures,
respectively, where the amplitude slowly decreases. In recent years, it has
been successfully applied to two combinatorial optimization tasks, the
traveling salesman problem and the search for low-energy states of the Coulomb
glass. In these cases, the algorithm is far more efficient than usual simulated
annealing. In its original form the algorithm was designed only for the case of
discrete variables. Its basic ideas are applicable also to a problem with
continuous variables, the search for low-energy states of Lennard-Jones
clusters. | cond-mat_dis-nn |
Ordering Behavior of the Two-Dimensional Ising Spin Glass with
Long-Range Correlated Disorder: The standard two-dimensional Ising spin glass does not exhibit an ordered
phase at finite temperature. Here, we investigate whether long-range correlated
bonds change this behavior. The bonds are drawn from a Gaussian distribution
with a two-point correlation for bonds at distance r that decays as
$(1+r^2)^{-a/2}$, $a>0$. We study numerically with exact algorithms the ground
state and domain wall excitations. Our results indicate that the inclusion of
bond correlations does not lead to a spin-glass order at any finite
temperature. A further analysis reveals that bond correlations have a strong
effect at local length scales, inducing ferro/antiferromagnetic domains into
the system. The length scale of ferro/antiferromagnetic order diverges
exponentially as the correlation exponent approaches a critical value, $a \to
a_c = 0$. Thus, our results suggest that the system becomes a
ferro/antiferromagnet only in the limit $a \to 0$. | cond-mat_dis-nn |
Coupling and Level Repulsion in the Localized Regime: From Isolated to
Quasi-Extended Modes: We study the interaction of Anderson localized states in an open 1D random
system by varying the internal structure of the sample. As the frequencies of
two states come close, they are transformed into multiply-peaked quasi-extended
modes. Level repulsion is observed experimentally and explained within a model
of coupled resonators. The spectral and spatial evolution of the coupled modes
is described in terms of the coupling coefficient and Q-factors of resonators. | cond-mat_dis-nn |
Absence of the non-percolating phase for percolation on the non-planar
Hanoi network: We investigate bond percolation on the non-planar Hanoi network (HN-NP),
which was studied in [Boettcher et al. Phys. Rev. E 80 (2009) 041115]. We
calculate the fractal exponent of a subgraph of the HN-NP, which gives a lower
bound for the fractal exponent of the original graph. This lower bound leads to
the conclusion that the original system does not have a non-percolating phase,
where only finite size clusters exist, for p>0, or equivalently, that the
system exhibits either the critical phase, where infinitely many infinite
clusters exist, or the percolating phase, where a unique giant component
exists. Monte Carlo simulations support our conjecture. | cond-mat_dis-nn |
Neural evolution structure generation: High Entropy Alloys: We propose a method of neural evolution structures (NESs) combining
artificial neural networks (ANNs) and evolutionary algorithms (EAs) to generate
High Entropy Alloys (HEAs) structures. Our inverse design approach is based on
pair distribution functions and atomic properties and allows one to train a
model on smaller unit cells and then generate a larger cell. With a speed-up
factor of approximately 1000 with respect to the SQSs, the NESs dramatically
reduces computational costs and time, making possible the generation of very
large structures (over 40,000 atoms) in few hours. Additionally, unlike the
SQSs, the same model can be used to generate multiple structures with the same
fractional composition. | cond-mat_dis-nn |
Anomalous Hall effect from a non-Hermitian viewpoint: Non-Hermitian descriptions often model open or driven systems away from the
equilibrium. Nonetheless, in equilibrium electronic systems, a non-Hermitian
nature of an effective Hamiltonian manifests itself as unconventional
observables such as a bulk Fermi arc and skin effects. We theoretically reveal
that spin-dependent quasiparticle lifetimes, which signify the non-Hermiticity
of an effective model in the equilibrium, induce the anomalous Hall effect,
namely the Hall effect without an external magnetic field. We first examine the
effect of nonmagnetic and magnetic impurities and obtain a non-Hermitian
effective model. Then, we calculate the Kubo formula from the microscopic model
to ascertain a non-Hermitian interpretation of the longitudinal and Hall
conductivities. Our results elucidate the vital role of the non-Hermitian
equilibrium nature in the quantum transport phenomena. | cond-mat_dis-nn |
Asymptotic Level Density of the Elastic Net Self-Organizing Feature Map: Whileas the Kohonen Self Organizing Map shows an asymptotic level density
following a power law with a magnification exponent 2/3, it would be desired to
have an exponent 1 in order to provide optimal mapping in the sense of
information theory. In this paper, we study analytically and numerically the
magnification behaviour of the Elastic Net algorithm as a model for
self-organizing feature maps. In contrast to the Kohonen map the Elastic Net
shows no power law, but for onedimensional maps nevertheless the density
follows an universal magnification law, i.e. depends on the local stimulus
density only and is independent on position and decouples from the stimulus
density at other positions. | cond-mat_dis-nn |
Dynamic relaxation of a liquid cavity under amorphous boundary
conditions: The growth of cooperatively rearranging regions was invoked long ago by Adam
and Gibbs to explain the slowing down of glass-forming liquids. The lack of
knowledge about the nature of the growing order, though, complicates the
definition of an appropriate correlation function. One option is the
point-to-set correlation function, which measures the spatial span of the
influence of amorphous boundary conditions on a confined system. By using a
swap Monte Carlo algorithm we measure the equilibration time of a liquid
droplet bounded by amorphous boundary conditions in a model glass-former at low
temperature, and we show that the cavity relaxation time increases with the
size of the droplet, saturating to the bulk value when the droplet outgrows the
point-to-set correlation length. This fact supports the idea that the
point-to-set correlation length is the natural size of the cooperatively
rearranging regions. On the other hand, the cavity relaxation time computed by
a standard, nonswap dynamics, has the opposite behavior, showing a very steep
increase when the cavity size is decreased. We try to reconcile this difference
by discussing the possible hybridization between MCT and activated processes,
and by introducing a new kind of amorphous boundary conditions, inspired by the
concept of frozen external state as an alternative to the commonly used frozen
external configuration. | cond-mat_dis-nn |
Phase diagram for the O(n) model with defects of "random local field"
type and verity of the Imry-Ma theorem: It is shown that the Imry-Ma theorem stating that in space dimensions d<4 the
introduction of an arbitrarily small concentration of defects of the "random
local field" type in a system with continuous symmetry of the n-component
vector order parameter (O(n)model) leads to the long-range order collapse and
to the occurrence of a disordered state, is not true if the anisotropic
distribution of the defect-induced random local field directions in the
n-dimensional space of the order parameter leads to the defect-induced
effective anisotropy of the "easy axis" type. For a weakly anisotropic field
distribution, in space dimensions 2<d<4 there exists some critical defect
concentration, above which the inhomogeneous Imry-Ma state can exist as an
equilibrium one. At lower defect concentration the long-range order takes place
in the system. For a strongly anisotropic field distribution, the Imry-Ma state
is suppressed completely and the long-range order state takes place at any
defect concentration. | cond-mat_dis-nn |
Cooperativity and Heterogeneity in Plastic Crystals Studied by Nonlinear
Dielectric Spectroscopy: The glassy dynamics of plastic-crystalline cyclo-octanol and ortho-carborane,
where only the molecular reorientational degrees of freedom freeze without
long-range order, is investigated by nonlinear dielectric spectroscopy. Marked
differences to canonical glass formers show up: While molecular cooperativity
governs the glassy freezing, it leads to a much weaker slowing down of
molecular dynamics than in supercooled liquids. Moreover, the observed
nonlinear effects cannot be explained with the same heterogeneity scenario
recently applied to canonical glass formers. This supports ideas that molecular
relaxation in plastic crystals may be intrinsically non-exponential. Finally,
no nonlinear effects were detected for the secondary processes in
cyclo-octanol. | cond-mat_dis-nn |
Many-body localization proximity effect in two-species bosonic Hubbard
model: The many-body localization (MBL) proximity effect is an intriguing phenomenon
where a thermal bath localizes due to the interaction with a disordered system.
The interplay of thermal and non-ergodic behavior in these systems gives rise
to a rich phase diagram, whose exploration is an active field of research. In
this work, we study a bosonic Hubbard model featuring two particle species
representing the bath and the disordered system. Using state of the art
numerical techniques, we investigate the dynamics of the model in different
regimes, based on which we obtain a tentative phase diagram as a function of
coupling strength and bath size. When the bath is composed of a single
particle, we observe clear signatures of a transition from an MBL proximity
effect to a delocalized phase. Increasing the bath size, however, its
thermalizing effect becomes stronger and eventually the whole system
delocalizes in the range of moderate interaction strengths studied. In this
regime, we characterize particle transport, revealing diffusive behavior of the
originally localized bosons. | cond-mat_dis-nn |
Apparent power-law behavior of conductance in disordered
quasi-one-dimensional systems: Dependence of hopping conductance on temperature and voltage for an ensemble
of modestly long one-dimensional wires is studied numerically using the
shortest-path algorithm. In a wide range of parameters this dependence can be
approximated by a power-law rather than the usual stretched-exponential form.
Relation to recent experiments and prior analytical theory is discussed. | cond-mat_dis-nn |
Clique percolation in random networks: The notion of k-clique percolation in random graphs is introduced, where k is
the size of the complete subgraphs whose large scale organizations are
analytically and numerically investigated. For the Erdos-Renyi graph of N
vertices we obtain that the percolation transition of k-cliques takes place
when the probability of two vertices being connected by an edge reaches the
threshold pc(k)=[(k-1)N]^{-1/(k-1)}. At the transition point the scaling of the
giant component with N is highly non-trivial and depends on k. We discuss why
clique percolation is a novel and efficient approach to the identification of
overlapping communities in large real networks. | cond-mat_dis-nn |
An improved Belief Propagation algorithm finds many Bethe states in the
random field Ising model on random graphs: We first present an empirical study of the Belief Propagation (BP) algorithm,
when run on the random field Ising model defined on random regular graphs in
the zero temperature limit. We introduce the notion of maximal solutions for
the BP equations and we use them to fix a fraction of spins in their ground
state configuration. At the phase transition point the fraction of
unconstrained spins percolates and their number diverges with the system size.
This in turn makes the associated optimization problem highly non trivial in
the critical region. Using the bounds on the BP messages provided by the
maximal solutions we design a new and very easy to implement BP scheme which is
able to output a large number of stable fixed points. On one side this new
algorithm is able to provide the minimum energy configuration with high
probability in a competitive time. On the other side we found that the number
of fixed points of the BP algorithm grows with the system size in the critical
region. This unexpected feature poses new relevant questions on the physics of
this class of models. | cond-mat_dis-nn |
Experimental Observation of a Fundamental Length Scale of Waves in
Random Media: Waves propagating through a weakly scattering random medium show a pronounced
branching of the flow accompanied by the formation of freak waves, i.e.,
extremely intense waves. Theory predicts that this strong fluctuation regime is
accompanied by its own fundamental length scale of transport in random media,
parametrically different from the mean free path or the localization length. We
show numerically how the scintillation index can be used to assess the scaling
behavior of the branching length. We report the experimental observation of
this scaling using microwave transport experiments in quasi-two-dimensional
resonators with randomly distributed weak scatterers. Remarkably, the scaling
range extends much further than expected from random caustics statistics. | cond-mat_dis-nn |
Optimization by thermal cycling: An optimization algorithm is presented which consists of cyclically heating
and quenching by Metropolis and local search procedures, respectively. It works
particularly well when it is applied to an archive of samples instead of to a
single one. We demonstrate for the traveling salesman problem that this
algorithm is far more efficient than usual simulated annealing; our
implementation can compete concerning speed with recent, very fast genetic
local search algorithms. | cond-mat_dis-nn |
Floquet-Anderson localization in the Thouless pump and how to avoid it: We investigate numerically how onsite disorder affects conduction in the
periodically driven Rice-Mele model, a prototypical realization of the Thouless
pump. Although the pump is robust against disorder in the fully adiabatic
limit, much less is known about the case of finite period time $T$, which is
relevant also in light of recent experimental realizations. We find that at any
fixed period time and nonzero disorder, increasing the system size $L\to\infty$
always leads to a breakdown of the pump, indicating Anderson localization of
the Floquet states. Our numerics indicate, however, that in a properly defined
thermodynamic limit, where $L/T^\theta$ is kept constant, Anderson localization
can be avoided, and the charge pumped per cycle has a well-defined value -- as
long as the disorder is not too strong. The critical exponent $\theta$ is not
universal, rather, its value depends on the disorder strength. Our findings are
relevant for practical, experimental realizations of the Thouless pump, for
studies investigating the nature of its current-carrying Floquet eigenstates,
as well as the mechanism of the full breakdown of the pump, expected if the
disorder exceeds a critical value. | cond-mat_dis-nn |
Creep and depinning in disordered media: Elastic systems driven in a disordered medium exhibit a depinning transition
at zero temperature and a creep regime at finite temperature and slow drive
$f$. We derive functional renormalization group equations which allow to
describe in details the properties of the slowly moving states in both cases.
Since they hold at finite velocity $v$, they allow to remedy some shortcomings
of the previous approaches to zero temperature depinning. In particular, they
enable us to derive the depinning law directly from the equation of motion,
with no artificial prescription or additional physical assumptions. Our
approach provides a controlled framework to establish under which conditions
the depinning regime is universal. It explicitly demonstrates that the random
potential seen by a moving extended system evolves at large scale to a random
field and yields a self-contained picture for the size of the avalanches
associated with the deterministic motion. At $T>0$ we find that the effective
barriers grow with lenghtscale as the energy differences between neighboring
metastable states, and demonstrate the resulting activated creep law $v\sim
\exp (-C f^{-\mu}/T)$ where the exponent $\mu$ is obtained in a $\epsilon=4-D$
expansion ($D$ is the internal dimension of the interface). Our approach also
provides quantitatively a new scenario for creep motion as it allows to
identify several intermediate lengthscales. In particular, we unveil a novel
``depinning-like'' regime at scales larger than the activation scale, with
avalanches spreading from the thermal nucleus scale up to the much larger
correlation length $R_{V}$. We predict that $R_{V}\sim T^{-\sigma}f^{-\lambda
}$ diverges at small $f$ and $T$ with exponents $\sigma ,\lambda$ that we
determine. | cond-mat_dis-nn |
Energy gaps in etched graphene nanoribbons: Transport measurements on an etched graphene nanoribbon are presented. It is
shown that two distinct voltage scales can be experimentally extracted that
characterize the parameter region of suppressed conductance at low charge
density in the ribbon. One of them is related to the charging energy of
localized states, the other to the strength of the disorder potential. The
lever arms of gates vary by up to 30% for different localized states which must
therefore be spread in position along the ribbon. A single-electron transistor
is used to prove the addition of individual electrons to the localized states.
In our sample the characteristic charging energy is of the order of 10 meV, the
characteristic strength of the disorder potential of the order of 100 meV. | cond-mat_dis-nn |
Delocalization of boundary states in disordered topological insulators: We use the method of bulk-boundary correspondence of topological invariants
to show that disordered topological insulators have at least one delocalized
state at their boundary at zero energy. Those insulators which do not have
chiral (sublattice) symmetry have in addition the whole band of delocalized
states at their boundary, with the zero energy state lying in the middle of the
band. This result was previously conjectured based on the anticipated
properties of the supersymmetric (or replicated) sigma models with WZW-type
terms, as well as verified in some cases using numerical simulations and a
variety of other arguments. Here we derive this result generally, in arbitrary
number of dimensions, and without relying on the description in the language of
sigma models. | cond-mat_dis-nn |
Critical eigenstates and their properties in one and two dimensional
quasicrystals: We present exact solutions for some eigenstates of hopping models on one and
two dimensional quasiperiodic tilings and show that they are "critical" states,
by explicitly computing their multifractal spectra. These eigenstates are shown
to be generically present in 1D quasiperiodic chains, of which the Fibonacci
chain is a special case. We then describe properties of the ground states for a
class of tight-binding Hamiltonians on the 2D Penrose and Ammann-Beenker
tilings. Exact and numerical solutions are seen to be in good agreement. | cond-mat_dis-nn |
Field-induced structural aging in glasses at ultra low temperatures: In non-equilibrium experiments on the glasses Mylar and BK7, we measured the
excess dielectric response after the temporary application of a strong electric
bias field at mK--temperatures. A model recently developed describes the
observed long time decays qualitatively for Mylar [PRL 90, 105501, S. Ludwig,
P. Nalbach, D. Rosenberg, D. Osheroff], but fails for BK7. In contrast, our
results on both samples can be described by including an additional mechanism
to the mentioned model with temperature independent decay times of the excess
dielectric response. As the origin of this novel process beyond the "tunneling
model" we suggest bias field induced structural rearrangements of "tunneling
states" that decay by quantum mechanical tunneling. | cond-mat_dis-nn |
Ising Model Scaling Behaviour on z-Preserving Small-World Networks: We have investigated the anomalous scaling behaviour of the Ising model on
small-world networks based on 2- and 3-dimensional lattices using Monte Carlo
simulations. Our main result is that even at low $p$, the shift in the critical
temperature $\Delta T_c$ scales as $p^{s}$, with $s \approx 0.50$ for 2-D
systems, $s \approx 0.698$ for 3-D and $s \approx 0.75$ for 4-D. We have also
verified that a $z$-preserving rewiring algorithm still exhibits small-world
effects and yet is more directly comparable with the conventional Ising model;
the small-world effect is due to enhanced long-range correlations and not the
change in effective dimension. We find the critical exponents $\beta$ and $\nu$
exhibit a monotonic change between an Ising-like transition and mean-field
behaviour in 2- and 3-dimensional systems. | cond-mat_dis-nn |
Fragmentation of a circular disc by projectiles: The fragmentation of a two-dimensional circular disc by lateral impact is
investigated using a cell model of brittle solid. The disc is composed of
numerous unbreakable randomly shaped convex polygons connected together by
simple elastic beams that break when bent or stretched beyond a certain limit.
We found that the fragment mass distribution follows a power law with an
exponent close to 2 independent of the system size. We also observed two types
of crack patterns: radial cracks starting from the impact point and cracks
perpendicular to the radial ones. Simulations revealed that there exists a
critical projectile energy, above which the target breaks into numerous smaller
pieces, and below which it suffers only damage in the form of cracks. Our
theoretical results are in a reasonable agreement with recent experimental
findings on the fragmentation of discs. | cond-mat_dis-nn |
Direct Measurement of Random Fields in the $LiHo_xY_{1-x}F_4$ Crystal: The random field Ising model (RFIM) is central to the study of disordered
systems. Yet, for a long time it eluded realization in ferromagnetic systems
because of the difficulty to produce locally random magnetic fields. Recently
it was shown that in anisotropic dipolar magnetic insulators, the archetypal of
which is the $LiHo_xY_{1-x}F_4$ system, the RFIM can be realized in both
ferromagnetic and spin glass phases. The interplay between an applied
transverse field and the offdiagonal terms of the dipolar interaction produce
effective longitudinal fields, which are random in sign and magnitude as a
result of spatial dilution. In this paper we use exact numerical
diagonalization of the full Hamiltonian of Ho pairs in $LiHo_xY_{1-x}F_4$ to
calculate the effective longitudinal field beyond the perturbative regime. In
particular, we find that nearby spins can experience an effective field larger
than the intrinsic dipolar broadening (of quantum states in zero field) which
can therefore be evidenced in experiments. We then calculate the magnetization
and susceptibility under several experimental protocols, and show how these
protocols can produce direct measurement of the effective longitudinal field. | cond-mat_dis-nn |
The Ising Spin Glass in dimension five: link overlaps: Extensive simulations are made of the link overlap in five dimensional Ising
Spin Glasses (ISGs) through and below the ordering transition. Moments of the
mean link overlap distributions (the kurtosis and the skewness) show clear
critical maxima at the ISG ordering temperature. These criteria can be used as
efficient tools to identify a freezing transition quite generally and in any
dimension. In the ISG ordered phase the mean link overlap distribution develops
a strong two peak structure, with the link overlap spectra of individual
samples becoming very heterogeneous. There is no tendency towards a "trivial"
universal single peak distribution in the range of size and temperature covered
by the data. | cond-mat_dis-nn |
Quantum exploration of high-dimensional canyon landscapes: Canyon landscapes in high dimension can be described as manifolds of small,
but extensive dimension, immersed in a higher dimensional ambient space and
characterized by a zero potential energy on the manifold. Here we consider the
problem of a quantum particle exploring a prototype of a high-dimensional
random canyon landscape. We characterize the thermal partition function and
show that around the point where the classical phase space has a satisfiability
transition so that zero potential energy canyons disappear, moderate quantum
fluctuations have a deleterious effect and induce glassy phases at temperature
where classical thermal fluctuations alone would thermalize the system.
Surprisingly we show that even when, classically, diffusion is expected to be
unbounded in space, the interplay between quantum fluctuations and the
randomness of the canyon landscape conspire to have a confining effect. | cond-mat_dis-nn |
Patterns of link reciprocity in directed networks: We address the problem of link reciprocity, the non-random presence of two
mutual links between pairs of vertices. We propose a new measure of reciprocity
that allows the ordering of networks according to their actual degree of
correlation between mutual links. We find that real networks are always either
correlated or anticorrelated, and that networks of the same type (economic,
social, cellular, financial, ecological, etc.) display similar values of the
reciprocity. The observed patterns are not reproduced by current models. This
leads us to introduce a more general framework where mutual links occur with a
conditional connection probability. In some of the studied networks we discuss
the form of the conditional connection probability and the size dependence of
the reciprocity. | cond-mat_dis-nn |
Finite-Temperature Fluid-Insulator Transition of Strongly Interacting 1D
Disordered Bosons: We consider the many-body localization-delocalization transition for strongly
interacting one- dimensional disordered bosons and construct the full picture
of finite temperature behavior of this system. This picture shows two
insulator-fluid transitions at any finite temperature when varying the
interaction strength. At weak interactions an increase in the interaction
strength leads to insulator->fluid transition, and for large interactions one
has a reentrance to the insulator regime. | cond-mat_dis-nn |
Excess wing in glass-forming glycerol and LiCl-glycerol mixtures
detected by neutron scattering: The relaxational dynamics in glass-forming glycerol and glycerol mixed with
LiCl is in-vestigated using different neutron scattering techniques. The
performed neutron spin-echo experiments, which extend up to relatively long
relaxation-time scales of the order of 10 ns, should allow for the detection of
contributions from the so-called excess wing. This phenomenon, whose
microscopic origin is controversially discussed, arises in a variety of glass
formers and, until now, was almost exclusively investigated by dielectric
spectros-copy and light scattering. Here we show that the relaxational process
causing the excess wing also can be detected by neutron scattering, which
directly couples to density fluctua-tions. | cond-mat_dis-nn |
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