text
stringlengths 89
2.49k
| category
stringclasses 19
values |
|---|---|
Statistics of cycles in large networks: We present a Markov Chain Monte Carlo method for sampling cycle length in
large graphs. Cycles are treated as microstates of a system with many degrees
of freedom. Cycle length corresponds to energy such that the length histogram
is obtained as the density of states from Metropolis sampling. In many growing
networks, mean cycle length increases algebraically with system size. The cycle
exponent $\alpha$ is characteristic of the local growth rules and not
determined by the degree exponent $\gamma$. For example, $\alpha=0.76(4)$ for
the Internet at the Autonomous Systems level. | cond-mat_dis-nn |
Strong Disorder Renewal Approach to DNA denaturation and wetting :
typical and large deviation properties of the free energy: For the DNA denaturation transition in the presence of random contact
energies, or equivalently the disordered wetting transition, we introduce a
Strong Disorder Renewal Approach to construct the optimal contacts in each
disordered sample of size $L$. The transition is found to be of infinite order,
with a correlation length diverging with the essential singularity $\ln \xi(T)
\propto |T-T_c |^{-1}$. In the critical region, we analyze the statistics over
samples of the free-energy density $f_L$ and of the contact density, which is
the order parameter of the transition. At the critical point, both decay as a
power-law of the length $L$ but remain distributed, in agreement with the
general phenomenon of lack of self-averaging at random critical points. We also
obtain that for any real $q>0$, the moment $\overline{Z_L^q} $ of order $q$ of
the partition function at the critical point is dominated by some exponentially
rare samples displaying a finite free-energy density, i.e. by the large
deviation sector of the probability distribution of the free-energy density. | cond-mat_dis-nn |
Water adsorption on amorphous silica surfaces: A Car-Parrinello
simulation study: A combination of classical molecular dynamics (MD) and ab initio
Car-Parrinello molecular dynamics (CPMD) simulations is used to investigate the
adsorption of water on a free amorphous silica surface. From the classical MD
SiO_2 configurations with a free surface are generated which are then used as
starting configurations for the CPMD.We study the reaction of a water molecule
with a two-membered ring at the temperature T=300K. We show that the result of
this reaction is the formation of two silanol groups on the surface. The
activation energy of the reaction is estimated and it is shown that the
reaction is exothermic. | cond-mat_dis-nn |
Nonlinear transmission and light localization in photonic crystal
waveguides: We study the light transmission in two-dimensional photonic crystal
waveguides with embedded nonlinear defects. First, we derive the effective
discrete equations with long-range interaction for describing the waveguide
modes, and demonstrate that they provide a highly accurate generalization of
the familiar tight-binding models which are employed, e.g., for the study of
the coupled-resonator optical waveguides. Using these equations, we investigate
the properties of straight waveguides and waveguide bends with embedded
nonlinear defects and demonstrate the possibility of the nonlinearity-induced
bistable transmission. Additionally, we study localized modes in the waveguide
bends and (linear and nonlinear) transmission of the bent waveguides and
emphasize the role of evanescent modes in these phenomena. | cond-mat_dis-nn |
Statistical mechanics of LDPC codes on channels with memory: We present an analytic method of assessing the typical performance of
low-density parity-check codes on finite-state Markov channels. We show that
this problem is similar to a spin-glass model on a `small-world' lattice. We
apply our methodology to binary-symmetric and binary-asymmetric channels and we
provide the critical noise levels for different degrees of channel symmetry. | cond-mat_dis-nn |
Stark many-body localization: We consider spinless fermions on a finite one-dimensional lattice,
interacting via nearest-neighbor repulsion and subject to a strong electric
field. In the non-interacting case, due to Wannier-Stark localization, the
single-particle wave functions are exponentially localized even though the
model has no quenched disorder. We show that this system remains localized in
the presence of interactions and exhibits physics analogous to models of
conventional many-body localization (MBL). In particular, the entanglement
entropy grows logarithmically with time after a quench, albeit with a slightly
different functional form from the MBL case, and the level statistics of the
many-body energy spectrum are Poissonian. We moreover predict that a quench
experiment starting from a charge-density wave state would show results similar
to those of Schreiber et al. [Science 349, 842 (2015)]. | cond-mat_dis-nn |
Experimental test of Sinai's model in DNA unzipping: The experimental measurement of correlation functions and critical exponents
in disordered systems is key to testing renormalization group (RG) predictions.
We mechanically unzip single DNA hairpins with optical tweezers, an
experimental realization of the diffusive motion of a particle in a
one-dimensional random force field, known as the Sinai model. We measure the
unzipping forces $F_w$ as a function of the trap position $w$ in equilibrium
and calculate the force-force correlator $\Delta_m(w)$, its amplitude, and
correlation length, finding agreement with theoretical predictions. We study
the universal scaling properties since the effective trap stiffness $m^2$
decreases upon unzipping. Fluctuations of the position of the base pair at the
unzipping junction $u$ scales as $u \sim m^{-\zeta}$, with a roughness exponent
$ \zeta=1.34\pm0.06$, in agreement with the analytical prediction $\zeta =
\frac{4}{3}$. Our study provides a single-molecule test of the functional RG
approach for disordered elastic systems in equilibrium. | cond-mat_dis-nn |
The Gardner transition in physical dimensions: The Gardner transition is the transition that at mean-field level separates a
stable glass phase from a marginally stable phase. This transition has
similarities with the de Almeida-Thouless transition of spin glasses. We have
studied a well-understood problem, that of disks moving in a narrow channel,
which shows many features usually associated with the Gardner transition.
However, we can show that some of these features are artifacts that arise when
a disk escapes its local cage during the quench to higher densities. There is
evidence that the Gardner transition becomes an avoided transition, in that the
correlation length becomes quite large, of order 15 particle diameters, even in
our quasi-one-dimensional system. | cond-mat_dis-nn |
Rayleigh anomalies and disorder-induced mixing of polarizations at
nanoscale in amorphous solids. Testing 1-octyl-3-methylimidazolium chloride
glass: Acoustic excitations in topologically disordered media at mesoscale present
anomalous features with respect to the Debye's theory. In a three-dimensional
medium an acoustic excitation is characterized by its phase velocity, intensity
and polarization. The so-called Rayleigh anomalies, which manifest in
attenuation and retardation of the acoustic excitations, affect the first two
properties. The topological disorder is, however, expected to influence also
the third one. Acoustic excitations with a well-defined polarization in the
continuum limit present indeed a so-called mixing of polarizations at
nanoscale, as attested by experimental observations and Molecular Dynamics
simulations. We provide a comprehensive experimental characterization of
acoustic dynamics properties of a selected glass, 1-octyl-3-methylimidazolium
chloride glass, whose heterogeneous structure at nanoscale is well-assessed.
Distinctive features, which can be related to the occurrence of the Rayleigh
anomalies and of the mixing of polarizations are observed. We develop, in the
framework of the Random Media Theory, an analytical model that allows a
quantitative description of all the Rayleigh anomalies and the mixing of
polarizations. Contrast between theoretical and experimental features for the
selected glass reveals an excellent agreement. The quantitative theoretical
approach permits thus to demonstrate how the mixing of polarizations generates
distinctive feature in the dynamic structure factor of glasses and to
unambiguously identify them. The robustness of the proposed theoretical
approach is validated by its ability to describe as well transverse acoustic
dynamics. | cond-mat_dis-nn |
Optimal Vertex Cover for the Small-World Hanoi Networks: The vertex-cover problem on the Hanoi networks HN3 and HN5 is analyzed with
an exact renormalization group and parallel-tempering Monte Carlo simulations.
The grand canonical partition function of the equivalent hard-core repulsive
lattice-gas problem is recast first as an Ising-like canonical partition
function, which allows for a closed set of renormalization group equations. The
flow of these equations is analyzed for the limit of infinite chemical
potential, at which the vertex-cover problem is attained. The relevant fixed
point and its neighborhood are analyzed, and non-trivial results are obtained
both, for the coverage as well as for the ground state entropy density, which
indicates the complex structure of the solution space. Using special
hierarchy-dependent operators in the renormalization group and Monte-Carlo
simulations, structural details of optimal configurations are revealed. These
studies indicate that the optimal coverages (or packings) are not related by a
simple symmetry. Using a clustering analysis of the solutions obtained in the
Monte Carlo simulations, a complex solution space structure is revealed for
each system size. Nevertheless, in the thermodynamic limit, the solution
landscape is dominated by one huge set of very similar solutions. | cond-mat_dis-nn |
Record breaking bursts during the compressive failure of porous
materials: An accurate understanding of the interplay between random and deterministic
processes in generating extreme events is of critical importance in many
fields, from forecasting extreme meteorological events to the catastrophic
failure of materials and in the Earth. Here we investigate the statistics of
record-breaking events in the time series of crackling noise generated by local
rupture events during the compressive failure of porous materials. The events
are generated by computer simulations of the uni-axial compression of
cylindrical samples in a discrete element model of sedimentary rocks that
closely resemble those of real experiments. The number of records grows
initially as a decelerating power law of the number of events, followed by an
acceleration immediately prior to failure. We demonstrate the existence of a
characteristic record rank k^* which separates the two regimes of the time
evolution. Up to this rank deceleration occurs due to the effect of random
disorder. Record breaking then accelerates towards macroscopic failure, when
physical interactions leading to spatial and temporal correlations dominate the
location and timing of local ruptures. Sub-sequences of bursts between
consecutive records are characterized by a power law size distribution with an
exponent which decreases as failure is approached. High rank records are
preceded by bursts of increasing size and waiting time between consecutive
events and they are followed by a relaxation process. As a reference, surrogate
time series are generated by reshuffling the crackling bursts. The record
statistics of the uncorrelated surrogates agrees very well with the
corresponding predictions of independent identically distributed random
variables, which confirms that the temporal and spatial correlation of cracking
bursts are responsible for the observed unique behaviour. | cond-mat_dis-nn |
Non equilibrium dynamics below the super-roughening transition: The non equilibrium relaxational dynamics of the solid on solid model on a
disordered substrate and the Sine Gordon model with random phase shifts is
studied numerically. Close to the super-roughening temperature $T_g$ our
results for the autocorrelations, spatial correlations and response function as
well as for the fluctuation dissipation ratio (FDR) agree well with the
prediction of a recent one loop RG calculation, whereas deep in the glassy low
temperature phase substantial deviations occur. The change in the low
temperature behavior of these quantities compared with the RG predictions is
shown to be contained in a change of the functional temperature dependence of
the dynamical exponent $z(T)$, which relates the age $t$ of the system with a
length scale ${\cal L}(t)$: $z(T)$ changes from a linear $T$-dependence close
to $T_g$ to a 1/T-behavior far away from $T_g$. By identifying spatial domains
as connected patches of the exactly computable ground states of the system we
demonstrate that the growing length scale ${\cal L}(t)$ is the characteristic
size of thermally fluctuating clusters around ``typical'' long-lived
configurations. | cond-mat_dis-nn |
Non-Abelian chiral symmetry controls random scattering in two-band
models: We study the dynamics of non-interacting quantum particles with two bands in
the presence of random scattering. The two bands are associated with a chiral
symmetry. After breaking the latter by a potential, we still find that the
quantum dynamics is controlled by a non-Abelian chiral symmetry. The
possibility of spontaneous symmetry breaking is analyzed within a
self-consistent approach, and the instability of a symmetric solution is
discussed. | cond-mat_dis-nn |
Fluctuation effects in metapopulation models: percolation and pandemic
threshold: Metapopulation models provide the theoretical framework for describing
disease spread between different populations connected by a network. In
particular, these models are at the basis of most simulations of pandemic
spread. They are usually studied at the mean-field level by neglecting
fluctuations. Here we include fluctuations in the models by adopting fully
stochastic descriptions of the corresponding processes. This level of
description allows to address analytically, in the SIS and SIR cases, problems
such as the existence and the calculation of an effective threshold for the
spread of a disease at a global level. We show that the possibility of the
spread at the global level is described in terms of (bond) percolation on the
network. This mapping enables us to give an estimate (lower bound) for the
pandemic threshold in the SIR case for all values of the model parameters and
for all possible networks. | cond-mat_dis-nn |
Memory effects, two color percolation, and the temperature dependence of
Mott's variable range hopping: There are three basic processes that determine hopping transport: (a) hopping
between normally empty sites (i.e. having exponentially small occupation
numbers at equilibrium); (b) hopping between normally occupied sites, and (c)
transitions between normally occupied and unoccupied sites. In conventional
theories all these processes are considered Markovian and the correlations of
occupation numbers of different sites are believed to be small(i.e. not
exponential in temperature). We show that, contrary to this belief, memory
effects suppress the processes of type (c), and manifest themselves in a
subleading {\em exponential} temperature dependence of the variable range
hopping conductivity. This temperature dependence originates from the property
that sites of type (a) and (b) form two independent resistor networks that are
weakly coupled to each other by processes of type (c). This leads to a
two-color percolation problem which we solve in the critical region. | cond-mat_dis-nn |
Molecular dynamics simulation of the fragile glass former
ortho-terphenyl: a flexible molecule model: We present a realistic model of the fragile glass former orthoterphenyl and
the results of extensive molecular dynamics simulations in which we
investigated its basic static and dynamic properties. In this model the
internal molecular interactions between the three rigid phenyl rings are
described by a set of force constants, including harmonic and anharmonic terms;
the interactions among different molecules are described by Lennard-Jones
site-site potentials. Self-diffusion properties are discussed in detail
together with the temperature and momentum dependencies of the
self-intermediate scattering function. The simulation data are compared with
existing experimental results and with the main predictions of the Mode
Coupling Theory. | cond-mat_dis-nn |
Percolation Thresholds of the Fortuin-Kasteleyn Cluster for a Potts
Gauge Glass Model on Complex Networks: Analytical Results on the Nishimori
Line: It was pointed out by de Arcangelis et al. [Europhys. Lett. 14 (1991), 515]
that the correct understanding of the percolation phenomenon of the
Fortuin-Kasteleyn cluster in the Edwards-Anderson model is important since a
dynamical transition, which is characterized by a parameter called the Hamming
distance or damage, and the percolation transition are related to a transition
for a signal propagating between spins. We show analytically the percolation
thresholds of the Fortuin-Kasteleyn cluster for a Potts gauge glass model,
which is an extended model of the Edwards-Anderson model, on random graphs with
arbitary degree distributions. The results are shown on the Nishimori line. We
also show the results for the infinite-range model. | cond-mat_dis-nn |
d=3 random field behavior near percolation: The highly diluted antiferromagnet Mn(0.35)Zn(0.65)F2 has been investigated
by neutron scattering for H>0. A low-temperature (T<11K), low-field (H<1T)
pseudophase transition boundary separates a partially antiferromagnetically
ordered phase from the paramagnetic one. For 1<H<7T at low temperatures, a
region of antiferromagnetic order is field induced but is not enclosed within a
transition boundary. | cond-mat_dis-nn |
Speckle intensity correlations of photons scattered by cold atoms: The irradiation of a dilute cloud of cold atoms with a coherent light field
produces a random intensity distribution known as laser speckle. Its
statistical fluctuations contain information about the mesoscopic scattering
processes at work inside the disordered medium. Following up on earlier work by
Assaf and Akkermans [Phys.\ Rev.\ Lett.\ \textbf{98}, 083601 (2007)], we
analyze how static speckle intensity correlations are affected by an internal
Zeeman degeneracy of the scattering atoms. It is proven on general grounds that
the speckle correlations cannot exceed the standard Rayleigh law. On the
contrary, because which-path information is stored in the internal atomic
states, the intensity correlations suffer from strong decoherence and become
exponentially small in the diffusive regime applicable to an optically thick
cloud. | cond-mat_dis-nn |
Critical localization with Van der Waals interactions: I discuss the quantum dynamics of strongly disordered quantum systems with
critically long range interactions, decaying as $1/r^{2d}$ in $d$ spatial
dimensions. I argue that, contrary to expectations, localization in such
systems is stable at low orders in perturbation theory, giving rise to an
unusual `critically many body localized regime.' I discuss the phenomenology of
this critical MBL regime, which includes distinctive signatures in
entanglement, charge statistics, noise, and transport. Experimentally, such a
critically localized regime can be realized in three dimensional systems with
Van der Waals interactions, such as Rydberg atoms, and in one dimensional
systems with $1/r^2$ interactions, such as trapped ions. I estimate timescales
on which high order perturbative and non-perturbative (avalanche) phenomena may
destabilize this critically MBL regime, and conclude that the avalanche sets
the limiting timescale, in the limit of strong disorder / weak interactions. | cond-mat_dis-nn |
Anderson localization and delocalization of massless two-dimensional
Dirac electrons in random one-dimensional scalar and vector potentials: We study Anderson localization of massless Dirac electrons in two dimensions
in one-dimensional random scalar and vector potentials theoretically for two
different cases, in which the scalar and vector potentials are either
uncorrelated or correlated. From the Dirac equation, we deduce the effective
wave impedance, using which we derive the condition for total transmission and
those for delocalization in our random models analytically. Based on the
invariant imbedding theory, we also develop a numerical method to calculate the
localization length exactly for arbitrary strengths of disorder. In addition,
we derive analytical expressions for the localization length, which are
extremely accurate in the weak and strong disorder limits. In the presence of
both scalar and vector potentials, the conditions for total transmission and
complete delocalization are generalized from the usual Klein tunneling case. We
find that the incident angles at which electron waves are either completely
transmitted or delocalized can be tuned to arbitrary values. When the strength
of scalar potential disorder increases to infinity, the localization length
also increases to infinity, both in uncorrelated and correlated cases. The
detailed dependencies of the localization length on incident angle, disorder
strength and energy are elucidated and the discrepancies with previous studies
and some new results are discussed. All the results are explained intuitively
using the concept of wave impedance. | cond-mat_dis-nn |
Lack of monotonicity in spin glass correlation functions: We study the response of a spin glass system with respect to the rescaling of
its interaction random variables and investigate numerically the behaviour of
the correlation functions with respect to the volume. While for a ferromagnet
the local energy correlation functions increase monotonically with the scale
and, by consequence, with respect to the volume of the system we find that in a
general spin glass model those monotonicities are violated. | cond-mat_dis-nn |
Critical dynamics of the k-core pruning process: We present the theory of the k-core pruning process (progressive removal of
nodes with degree less than k) in uncorrelated random networks. We derive exact
equations describing this process and the evolution of the network structure,
and solve them numerically and, in the critical regime of the process,
analytically. We show that the pruning process exhibits three different
behaviors depending on whether the mean degree <q> of the initial network is
above, equal to, or below the threshold <q>_c corresponding to the emergence of
the giant k-core. We find that above the threshold the network relaxes
exponentially to the k-core. The system manifests the phenomenon known as
"critical slowing down", as the relaxation time diverges when <q> tends to
<q>_c. At the threshold, the dynamics become critical characterized by a
power-law relaxation (1/t^2). Below the threshold, a long-lasting transient
process (a "plateau" stage) occurs. This transient process ends with a collapse
in which the entire network disappears completely. The duration of the process
diverges when <q> tends to <q>_c. We show that the critical dynamics of the
pruning are determined by branching processes of spreading damage. Clusters of
nodes of degree exactly k are the evolving substrate for these branching
processes. Our theory completely describes this branching cascade of damage in
uncorrelated networks by providing the time dependent distribution function of
branching. These theoretical results are supported by our simulations of the
$k$-core pruning in Erdos-Renyi graphs. | cond-mat_dis-nn |
New class of level statistics in correlated disordered chains: We study the properties of the level statistics of 1D disordered systems with
long-range spatial correlations. We find a threshold value in the degree of
correlations below which in the limit of large system size the level statistics
follows a Poisson distribution (as expected for 1D uncorrelated disordered
systems), and above which the level statistics is described by a new class of
distribution functions. At the threshold, we find that with increasing system
size the standard deviation of the function describing the level statistics
converges to the standard deviation of the Poissonian distribution as a power
law. Above the threshold we find that the level statistics is characterized by
different functional forms for different degrees of correlations. | cond-mat_dis-nn |
Universal correlations between shocks in the ground state of elastic
interfaces in disordered media: The ground state of an elastic interface in a disordered medium undergoes
collective jumps upon variation of external parameters. These mesoscopic jumps
are called shocks, or static avalanches. Submitting the interface to a
parabolic potential centered at $w$, we study the avalanches which occur as $w$
is varied. We are interested in the correlations between the avalanche sizes
$S_1$ and $S_2$ occurring at positions $w_1$ and $w_2$. Using the Functional
Renormalization Group (FRG), we show that correlations exist for realistic
interface models below their upper critical dimension. Notably, the connected
moment $ \langle S_1 S_2 \rangle^c$ is up to a prefactor exactly the
renormalized disorder correlator, itself a function of $|w_2-w_1|$. The latter
is the universal function at the center of the FRG; hence correlations between
shocks are universal as well. All moments and the full joint probability
distribution are computed to first non-trivial order in an $\epsilon$-expansion
below the upper critical dimension. To quantify the local nature of the
coupling between avalanches, we calculate the correlations of their local
jumps. We finally test our predictions against simulations of a particle in
random-bond and random-force disorder, with surprisingly good agreement. | cond-mat_dis-nn |
Derivatives and inequalities for order parameters in the Ising spin
glass: Identities and inequalities are proved for the order parameters, correlation
functions and their derivatives of the Ising spin glass. The results serve as
additional evidence that the ferromagnetic phase is composed of two regions,
one with strong ferromagnetic ordering and the other with the effects of
disorder dominant. The Nishimori line marks a crossover between these two
regions. | cond-mat_dis-nn |
Metastable states in disordered Ising magnets in mean-field
approximation: The mechanism of appearance of exponentially large number of metastable
states in magnetic phases of disordered Ising magnets with short-range random
exchange is suggested. It is based on the assumption that transitions into
inhomogeneous magnetic phases results from the condensation of macroscopically
large number of sparse delocalized modes near the localization threshold. The
properties of metastable states in random magnets with zero ground state
magnetization (dilute antiferromagnet, binary spin glass, dilute ferromagnet
with dipole interaction) has been obtained in framework of this mechanism using
variant of mean-field approximation. The relations between the characteristics
of slow nonequilibrium processes in magnetic phases and thermodynamic
parameters of metastable states are established. | cond-mat_dis-nn |
Spreading in Disordered Lattices with Different Nonlinearities: We study the spreading of initially localized states in a nonlinear
disordered lattice described by the nonlinear Schr\"odinger equation with
random on-site potentials - a nonlinear generalization of the Anderson model of
localization. We use a nonlinear diffusion equation to describe the
subdiffusive spreading. To confirm the self-similar nature of the evolution we
characterize the peak structure of the spreading states with help of R\'enyi
entropies and in particular with the structural entropy. The latter is shown to
remain constant over a wide range of time. Furthermore, we report on the
dependence of the spreading exponents on the nonlinearity index in the
generalized nonlinear Schr\"odinger disordered lattice, and show that these
quantities are in accordance with previous theoretical estimates, based on
assumptions of weak and very weak chaoticity of the dynamics. | cond-mat_dis-nn |
Percolation Transition in a Topological Phase: Transition out of a topological phase is typically characterized by
discontinuous changes in topological invariants along with bulk gap closings.
However, as a clean system is geometrically punctured, it is natural to ask the
fate of an underlying topological phase. To understand this physics we
introduce and study both short and long-ranged toy models where a one
dimensional topological phase is subjected to bond percolation protocols. We
find that non-trivial boundary phenomena follow competing energy scales even
while global topological response is governed via geometrical properties of the
percolated lattice. Using numerical, analytical and appropriate mean-field
studies we uncover the rich phenomenology and the various cross-over regimes of
these systems. In particular, we discuss emergence of "fractured topological
region" where an overall trivial system contains macroscopic number of
topological clusters. Our study shows the interesting physics that can arise
from an interplay of geometrical disorder within a topological phase. | cond-mat_dis-nn |
The dipolar spin glass transition in three dimensions: Dilute dipolar Ising magnets remain a notoriously hard problem to tackle both
analytically and numerically because of long-ranged interactions between spins
as well as rare region effects. We study a new type of anisotropic dilute
dipolar Ising system in three dimensions [Phys. Rev. Lett. {\bf 114}, 247207
(2015)] that arises as an effective description of randomly diluted classical
spin ice, a prototypical spin liquid in the disorder-free limit, with a small
fraction $x$ of non-magnetic impurities. Metropolis algorithm within a parallel
thermal tempering scheme fails to achieve equilibration for this problem
already for small system sizes. Motivated by previous work [Phys. Rev. X {\bf
4}, 041016 (2014)] on uniaxial random dipoles, we present an improved cluster
Monte Carlo algorithm that is tailor-made for removing the equilibration
bottlenecks created by clusters of {\it effectively frozen} spins. By
performing large-scale simulations down to $x=1/128$ and using finite size
scaling, we show the existence of a finite-temperature spin glass transition
and give strong evidence that the universality of the critical point is
independent of $x$ when it is small. In this $x \ll 1$ limit, we also provide a
first estimate of both the thermal exponent, $\nu=1.27(8)$, and the anomalous
exponent, $\eta=0.228(35)$. | cond-mat_dis-nn |
Anderson localization of emergent quasiparticles: Spinon and vison
interplay at finite temperature in a $\mathbb{Z}_2$ gauge theory in three
dimensions: Fractional statistics of quasiparticle excitations often plays an important
role in the detection and characterization of topological systems. In this
paper, we investigate the case of a three-dimensional (3D) Z2 gauge theory,
where the excitations take the form of bosonic spinon quasiparticle and vison
flux tubes, with mutual semionic statistics. We focus on an experimentally
relevant intermediate temperature regime, where sparse spinons hop coherently
on a dense quasistatic and stochastic vison background. The effective
Hamiltonian reduces to a random-sign bimodal tight-binding model, where both
the particles and the disorder are borne out of the same underlying quantum
spin liquid (QSL) degrees of freedom, and the coupling between the two is
purely driven by the mutual fractional statistics. We study the localization
properties and observe a mobility edge located close to the band edge, whose
transition belongs to the 3D Anderson model universality class. Spinons allowed
to propagate through the quasistatic vison background appear to display quantum
diffusive behavior. When the visons are allowed to relax, in response to the
presence of spinons in equilibrium, we observe the formation of vison depletion
regions slave to the support of the spinon wavefunction. We discuss how this
behavior can give rise to measurable effects in the relaxation, response and
transport properties of the system and how these may be used as signatures of
the mutual semionic statistics and as precursors of the QSL phase arising in
the system at lower temperatures. | cond-mat_dis-nn |
Enhancing the spectral gap of networks by node removal: Dynamics on networks are often characterized by the second smallest
eigenvalue of the Laplacian matrix of the network, which is called the spectral
gap. Examples include the threshold coupling strength for synchronization and
the relaxation time of a random walk. A large spectral gap is usually
associated with high network performance, such as facilitated synchronization
and rapid convergence. In this study, we seek to enhance the spectral gap of
undirected and unweighted networks by removing nodes because, practically, the
removal of nodes often costs less than the addition of nodes, addition of
links, and rewiring of links. In particular, we develop a perturbative method
to achieve this goal. The proposed method realizes better performance than
other heuristic methods on various model and real networks. The spectral gap
increases as we remove up to half the nodes in most of these networks. | cond-mat_dis-nn |
Localization Transition in Incommensurate non-Hermitian Systems: A class of one-dimensional lattice models with incommensurate complex
potential $V(\theta)=2[\lambda_r cos(\theta)+i \lambda_i sin(\theta)]$ is found
to exhibit localization transition at $|\lambda_r|+|\lambda_i|=1$. This
transition from extended to localized states manifests in the behavior of the
complex eigenspectum. In the extended phase, states with real eigenenergies
have finite measure and this measure goes to zero in the localized phase.
Furthermore, all extended states exhibit real spectrum provided $|\lambda_r|
\ge |\lambda_i|$. Another novel feature of the system is the fact that the
imaginary part of the spectrum is sensitive to the boundary conditions {\it
only at the onset to localization}. | cond-mat_dis-nn |
Mean field theory for the three-dimensional Coulomb glass: We study the low temperature phase of the 3D Coulomb glass within a mean
field approach which reduces the full problem to an effective single site model
with a non-trivial replica structure. We predict a finite glass transition
temperature $T_c$, and a glassy low temperature phase characterized by
permanent criticality. The latter is shown to assure the saturation of the
Efros-Shklovskii Coulomb gap in the density of states. We find this pseudogap
to be universal due to a fixed point in Parisi's flow equations. The latter is
given a physical interpretation in terms of a dynamical self-similarity of the
system in the long time limit, shedding new light on the concept of effective
temperature. From the low temperature solution we infer properties of the
hierarchical energy landscape, which we use to make predictions about the
master function governing the aging in relaxation experiments. | cond-mat_dis-nn |
Finite size scaling in neural networks: We demonstrate that the fraction of pattern sets that can be stored in
single- and hidden-layer perceptrons exhibits finite size scaling. This feature
allows to estimate the critical storage capacity \alpha_c from simulations of
relatively small systems. We illustrate this approach by determining \alpha_c,
together with the finite size scaling exponent \nu, for storing Gaussian
patterns in committee and parity machines with binary couplings and up to K=5
hidden units. | cond-mat_dis-nn |
Phase transitions in diluted negative-weight percolation models: We investigate the geometric properties of loops on two-dimensional lattice
graphs, where edge weights are drawn from a distribution that allows for
positive and negative weights. We are interested in the appearance of spanning
loops of total negative weight. The resulting percolation problem is
fundamentally different from conventional percolation, as we have seen in a
previous study of this model for the undiluted case.
Here, we investigate how the percolation transition is affected by additional
dilution. We consider two types of dilution: either a certain fraction of edges
exhibit zero weight, or a fraction of edges is even absent. We study these
systems numerically using exact combinatorial optimization techniques based on
suitable transformations of the graphs and applying matching algorithms. We
perform a finite-size scaling analysis to obtain the phase diagram and
determine the critical properties of the phase boundary.
We find that the first type of dilution does not change the universality
class compared to the undiluted case whereas the second type of dilution leads
to a change of the universality class. | cond-mat_dis-nn |
Influence of disorder on a Bragg microcavity: Using the resonant-state expansion for leaky optical modes of a planar Bragg
microcavity, we investigate the influence of disorder on its fundamental cavity
mode. We model the disorder by randomly varying the thickness of the Bragg-pair
slabs (composing the mirrors) and the cavity, and calculate the resonant energy
and linewidth of each disordered microcavity exactly, comparing the results
with the resonant-state expansion for a large basis set and within its first
and second orders of perturbation theory. We show that random shifts of
interfaces cause a growth of the inhomogeneous broadening of the fundamental
mode that is proportional to the magnitude of disorder. Simultaneously, the
quality factor of the microcavity decreases inversely proportional to the
square of the magnitude of disorder. We also find that first-order perturbation
theory works very accurately up to a reasonably large disorder magnitude,
especially for calculating the resonance energy, which allows us to derive
qualitatively the scaling of the microcavity properties with disorder strength. | cond-mat_dis-nn |
Self-organized criticality in neural network models: It has long been argued that neural networks have to establish and maintain a
certain intermediate level of activity in order to keep away from the regimes
of chaos and silence. Strong evidence for criticality has been observed in
terms of spatio-temporal activity avalanches first in cultures of rat cortex by
Beggs and Plenz (2003) and subsequently in many more experimental setups. These
findings sparked intense research on theoretical models for criticality and
avalanche dynamics in neural networks, where usually some dynamical order
parameter is fed back onto the network topology by adapting the synaptic
couplings. We here give an overview of existing theoretical models of dynamical
networks. While most models emphasize biological and neurophysiological detail,
our path here is different: we pick up the thread of an early self-organized
critical neural network model by Bornholdt and Roehl (2001) and test its
applicability in the light of experimental data. Keeping the simplicity of
early models, and at the same time lifting the drawback of a spin formulation
with respect to the biological system, we here study an improved model
(Rybarsch and Bornholdt, 2012b) and show that it adapts to criticality
exhibiting avalanche statistics that compare well with experimental data
without the need for parameter tuning. | cond-mat_dis-nn |
Avalanches and perturbation theory in the random-field Ising model: Perturbation theory for the random-field Ising model (RFIM) has the infamous
attribute that it predicts at all orders a dimensional-reduction property for
the critical behavior that turns out to be wrong in low dimension. Guided by
our previous work based on the nonperturbative functional renormalization group
(NP-FRG), we show that one can still make some use of the perturbation theory
for a finite range of dimension below the upper critical dimension, d=6. The
new twist is to account for the influence of large-scale zero-temperature
events known as avalanches. These avalanches induce nonanalyticities in the
field dependence of the correlation functions and renormalized vertices, and we
compute in a loop expansion the eigenvalue associated with the corresponding
anomalous operator. The outcome confirms the NP-FRG prediction that the
dimensional-reduction fixed point correctly describes the dominant critical
scaling of the RFIM above some dimension close to 5 but not below. | cond-mat_dis-nn |
Spectral properties of complex networks: This review presents an account of the major works done on spectra of
adjacency matrices drawn on networks and the basic understanding attained so
far. We have divided the review under three sections: (a) extremal eigenvalues,
(b) bulk part of the spectrum and (c) degenerate eigenvalues, based on the
intrinsic properties of eigenvalues and the phenomena they capture. We have
reviewed the works done for spectra of various popular model networks, such as
the Erd\H{o}s-R\'enyi random networks, scale-free networks, 1-d lattice,
small-world networks, and various different real-world networks. Additionally,
potential applications of spectral properties for natural processes have been
reviewed. | cond-mat_dis-nn |
Erratum: Small-world networks: Evidence for a crossover picture: We correct the value of the exponent \tau. | cond-mat_dis-nn |
Onset of reptations and critical hysteretic behavior in disordered
systems: Zero-temperature random coercivity Ising model with antiferromagnetic-like
interactions is used to study closure of minor hysteresis loops and wiping-out
property (Return Point Memory) in hysteretic behavior. Numerical simulations in
two dimensions as well as mean-field modeling show a critical phenomenon in the
hysteretic behavior associated with the loss of minor loop closure and the
onset of reptations. Power law scaling of the extent of minor loop reptations
is observed. | cond-mat_dis-nn |
The September 11 Attack: A Percolation of Individual Passive Support: A model for terrorism is presented using the theory of percolation. Terrorism
power is related to the spontaneous formation of random backbones of people who
are sympathetic to terrorism but without being directly involved in it. They
just don't oppose in case they could. In the past such friendly-to-terrorism
backbones have been always existing but were of finite size and localized to a
given geographical area. The September 11 terrorist attack on the US has
revealed for the first time the existence of a world wide spread extension. It
is argued to have result from a sudden world percolation of otherwise
unconnected and dormant world spread backbones of passive supporters. The
associated strategic question is then to determine if collecting ground
information could have predict and thus avoid such a transition. Our results
show the answer is no, voiding the major criticism against intelligence
services. To conclude the impact of military action is discussed. | cond-mat_dis-nn |
A tomography of the GREM: beyond the REM conjecture: Recently, Bauke and Mertens conjectured that the local statistics of energies
in random spin systems with discrete spin space should in most circumstances be
the same as in the random energy model. This was proven in a large class of
models for energies that do not grow too fast with the system size. Considering
the example of the generalized random energy model, we show that the conjecture
breaks down for energies proportional to the volume of the system, and describe
the far more complex behavior that then sets in. | cond-mat_dis-nn |
Renormalization for Discrete Optimization: The renormalization group has proven to be a very powerful tool in physics
for treating systems with many length scales. Here we show how it can be
adapted to provide a new class of algorithms for discrete optimization. The
heart of our method uses renormalization and recursion, and these processes are
embedded in a genetic algorithm. The system is self-consistently optimized on
all scales, leading to a high probability of finding the ground state
configuration. To demonstrate the generality of such an approach, we perform
tests on traveling salesman and spin glass problems. The results show that our
``genetic renormalization algorithm'' is extremely powerful. | cond-mat_dis-nn |
Interference phenomena in radiation of a charged particle moving in a
system with one-dimensional randomness: The contribution of interference effects to the radiation of a charged
particle moving in a medium of randomly spaced plates is considered. In the
angular dependent radiation intensity a peak appears at angles
$\theta\sim\pi-\gamma^{-1}$, where $\gamma$ is the Lorentz factor of the
charged particle. | cond-mat_dis-nn |
On the Paramagnetic Impurity Concentration of Silicate Glasses from
Low-Temperature Physics: The concentration of paramagnetic trace impurities in glasses can be
determined via precise SQUID measurements of the sample's magnetization in a
magnetic field. However the existence of quasi-ordered structural
inhomogeneities in the disordered solid causes correlated tunneling currents
that can contribute to the magnetization, surprisingly, also at the higher
temperatures. We show that taking into account such tunneling systems gives
rise to a good agreement between the concentrations extracted from SQUID
magnetization and those extracted from low-temperature heat capacity
measurements. Without suitable inclusion of such magnetization contribution
from the tunneling currents we find that the concentration of paramagnetic
impurities gets considerably over-estimated. This analysis represents a further
positive test for the structural inhomogeneity theory of the magnetic effects
in the cold glasses. | cond-mat_dis-nn |
Universality class of 3D site-diluted and bond-diluted Ising systems: We present a finite-size scaling analysis of high-statistics Monte Carlo
simulations of the three-dimensional randomly site-diluted and bond-diluted
Ising model. The critical behavior of these systems is affected by
slowly-decaying scaling corrections which make the accurate determination of
their universal asymptotic behavior quite hard, requiring an effective control
of the scaling corrections. For this purpose we exploit improved Hamiltonians,
for which the leading scaling corrections are suppressed for any thermodynamic
quantity, and improved observables, for which the leading scaling corrections
are suppressed for any model belonging to the same universality class.
The results of the finite-size scaling analysis provide strong numerical
evidence that phase transitions in three-dimensional randomly site-diluted and
bond-diluted Ising models belong to the same randomly dilute Ising universality
class. We obtain accurate estimates of the critical exponents, $\nu=0.683(2)$,
$\eta=0.036(1)$, $\alpha=-0.049(6)$, $\gamma=1.341(4)$, $\beta=0.354(1)$,
$\delta=4.792(6)$, and of the leading and next-to-leading correction-to-scaling
exponents, $\omega=0.33(3)$ and $\omega_2=0.82(8)$. | cond-mat_dis-nn |
Comment on "Quantum and Classical Glass Transitions in
LiHo$_{x}$Y$_{1-x}$F$_4$" by C. Ancona-Torres, D.M. Silevitch, G. Aeppli, and
T. F. Rosenbaum, Phys. Rev. Lett. 101, 057201 (2008): We show in this comment that the claim by Ancona-Torres et al. of an
equilibrium quantum or classical phase transition in the LiHo$_x$Y$_{1-x}$F$_4$
system is not supported by a rigorous scaling analysis. | cond-mat_dis-nn |
Beyond universal behavior in the one-dimensional chain with random
nearest neighbor hopping: We study the one-dimensional nearest neighbor tight binding model of
electrons with independently distributed random hopping and no on-site
potential (i.e. off-diagonal disorder with particle-hole symmetry, leading to
sub-lattice symmetry, for each realization). For non-singular distributions of
the hopping, it is known that the model exhibits a universal, singular behavior
of the density of states $\rho(E) \sim 1/|E \ln^3|E||$ and of the localization
length $\xi(E) \sim |\ln|E||$, near the band center $E = 0$. (This singular
behavior is also applicable to random XY and Heisenberg spin chains; it was
first obtained by Dyson for a specific random harmonic oscillator chain).
Simultaneously, the state at $E = 0$ shows a universal, sub-exponential decay
at large distances $\sim \exp [ -\sqrt{r/r_0} ]$. In this study, we consider
singular, but normalizable, distributions of hopping, whose behavior at small
$t$ is of the form $\sim 1/ [t \ln^{\lambda+1}(1/t) ]$, characterized by a
single, continuously tunable parameter $\lambda > 0$. We find, using a
combination of analytic and numerical methods, that while the universal result
applies for $\lambda > 2$, it no longer holds in the interval $0 < \lambda <
2$. In particular, we find that the form of the density of states singularity
is enhanced (relative to the Dyson result) in a continuous manner depending on
the non-universal parameter $\lambda$; simultaneously, the localization length
shows a less divergent form at low energies, and ceases to diverge below
$\lambda = 1$. For $\lambda < 2$, the fall-off of the $E = 0$ state at large
distances also deviates from the universal result, and is of the form $\sim
\exp [-(r/r_0)^{1/\lambda}]$, which decays faster than an exponential for
$\lambda < 1$. | cond-mat_dis-nn |
Super-diffusion in optical realizations of Anderson localization: We discuss the dynamics of particles in one dimension in potentials that are
random both in space and in time. The results are applied to recent optics
experiments on Anderson localization, in which the transverse spreading of a
beam is suppressed by random fluctuations in the refractive index. If the
refractive index fluctuates along the direction of the paraxial propagation of
the beam, the localization is destroyed. We analyze this broken localization,
in terms of the spectral decomposition of the potential. When the potential has
a discrete spectrum, the spread is controlled by the overlap of Chirikov
resonances in phase space. As the number of Fourier components is increased,
the resonances merge into a continuum, which is described by a Fokker-Planck
equation. We express the diffusion coefficient in terms of the spectral
intensity of the potential. For a general class of potentials that are commonly
used in optics, the solutions of the Fokker-Planck equation exhibit anomalous
diffusion in phase space, implying that when Anderson localization is broken by
temporal fluctuations of the potential, the result is transport at a rate
similar to a ballistic one or even faster. For a class of potentials which
arise in some existing realizations of Anderson localization atypical behavior
is found. | cond-mat_dis-nn |
AC-field-controlled localization-delocalization transition in one
dimensional disordered system: Based on the random dimer model, we study correlated disorder in a one
dimensional system driven by a strong AC field. As the correlations in a random
system may generate extended states and enhance transport in DC fields, we
explore the role that AC fields have on these properties. We find that similar
to ordered structures, AC fields renormalize the effective hopping constant to
a smaller value, and thus help to localize a state. We find that AC fields
control then a localization-delocalization transition in a given one
dimensional systems with correlated disorder. The competition between band
renormalization (band collapse/dynamic localization), Anderson localization,
and the structure correlation is shown to result in interesting transport
properties. | cond-mat_dis-nn |
Minimum spanning trees on weighted scale-free networks: A complete understanding of real networks requires us to understand the
consequences of the uneven interaction strengths between a system's components.
Here we use the minimum spanning tree (MST) to explore the effect of weight
assignment and network topology on the organization of complex networks. We
find that if the weight distribution is correlated with the network topology,
the MSTs are either scale-free or exponential. In contrast, when the
correlations between weights and topology are absent, the MST degree
distribution is a power-law and independent of the weight distribution. These
results offer a systematic way to explore the impact of weak links on the
structure and integrity of complex networks. | cond-mat_dis-nn |
Calorimetric glass transition in a mean field theory approach: The study of the properties of glass-forming liquids is difficult for many
reasons. Analytic solutions of mean field models are usually available only for
systems embedded in a space with an unphysically high number of spatial
dimensions; on the experimental and numerical side, the study of the properties
of metastable glassy states requires to thermalize the system in the
supercooled liquid phase, where the thermalization time may be extremely large.
We consider here an hard-sphere mean field model which is solvable in any
number of spatial dimensions; moreover we easily obtain thermalized
configurations even in the glass phase. We study the three dimensional version
of this model and we perform Monte Carlo simulations which mimic heating and
cooling experiments performed on ultra-stable glasses. The numerical findings
are in good agreement with the analytical results and qualitatively capture the
features of ultra-stable glasses observed in experiments. | cond-mat_dis-nn |
Second order phase transition in the six-dimensional Ising spin glass on
a field: The very existence of a phase transition for spin glasses in an external
magnetic field is controversial, even in high dimensions. We carry out massive
simulations of the Ising spin-glass in a field, in six dimensions (which,
according to classical, but not generally accepted, field-theoretical studies,
is the upper critical dimension). We find a phase transition and compute the
critical exponents, that are found to be compatible with their mean-field
values. We also find that the replica-symmetric Hamiltonian describes the
scaling of the renormalized couplings near the phase transition. | cond-mat_dis-nn |
Slow and Long-ranged Dynamical Heterogeneities in Dissipative Fluids: A two-dimensional bidisperse granular fluid is shown to exhibit pronounced
long-ranged dynamical heterogeneities as dynamical arrest is approached. Here
we focus on the most direct approach to study these heterogeneities: we
identify clusters of slow particles and determine their size, $N_c$, and their
radius of gyration, $R_G$. We show that $N_c\propto R_G^{d_f}$, providing
direct evidence that the most immobile particles arrange in fractal objects
with a fractal dimension, $d_f$, that is observed to increase with packing
fraction $\phi$. The cluster size distribution obeys scaling, approaching an
algebraic decay in the limit of structural arrest, i.e., $\phi\to\phi_c$.
Alternatively, dynamical heterogeneities are analyzed via the four-point
structure factor $S_4(q,t)$ and the dynamical susceptibility $\chi_4(t)$.
$S_4(q,t)$ is shown to obey scaling in the full range of packing fractions,
$0.6\leq\phi\leq 0.805$, and to become increasingly long-ranged as
$\phi\to\phi_c$. Finite size scaling of $\chi_4(t)$ provides a consistency
check for the previously analyzed divergences of $\chi_4(t)\propto
(\phi-\phi_c)^{-\gamma_{\chi}}$ and the correlation length $\xi\propto
(\phi-\phi_c)^{-\gamma_{\xi}}$. We check the robustness of our results with
respect to our definition of mobility. The divergences and the scaling for
$\phi\to\phi_c$ suggest a non-equilibrium glass transition which seems
qualitatively independent of the coefficient of restitution. | cond-mat_dis-nn |
Entanglement entropy of random partitioning: We study the entanglement entropy of random partitions in one- and
two-dimensional critical fermionic systems. In an infinite system we consider a
finite, connected (hypercubic) domain of linear extent $L$, the points of which
with probability $p$ belong to the subsystem. The leading contribution to the
average entanglement entropy is found to scale with the volume as $a(p) L^D$,
where $a(p)$ is a non-universal function, to which there is a logarithmic
correction term, $b(p)L^{D-1}\ln L$. In $1D$ the prefactor is given by
$b(p)=\frac{c}{3} f(p)$, where $c$ is the central charge of the model and
$f(p)$ is a universal function. In $2D$ the prefactor has a different
functional form of $p$ below and above the percolation threshold. | cond-mat_dis-nn |
Short-range Magnetic interactions in the Spin-Ice compound
Ho$_{2}$Ti$_{2}$O$_{7}$: Magnetization and susceptibility studies on single crystals of the pyrochlore
Ho$_{2}$Ti$_{2}$O$_{7}$ are reported for the first time. Magnetization
isotherms are shown to be qualitatively similar to that predicted by the
nearest neighbor spin-ice model. Below the lock-in temperature, $T^{\ast
}\simeq 1.97$ K, magnetization is consistent with the locking of spins along
[111] directions in a specific two-spins-in, two-spins-out arrangement. Below
$T^{\ast}$ the magnetization for $B||[111]$ displays a two step behavior
signalling the breaking of the ice rules. | cond-mat_dis-nn |
Method to solve quantum few-body problems with artificial neural
networks: A machine learning technique to obtain the ground states of quantum few-body
systems using artificial neural networks is developed. Bosons in continuous
space are considered and a neural network is optimized in such a way that when
particle positions are input into the network, the ground-state wave function
is output from the network. The method is applied to the Calogero-Sutherland
model in one-dimensional space and Efimov bound states in three-dimensional
space. | cond-mat_dis-nn |
Comprehensive study of the critical behavior in the diluted
antiferromagnet in a field: We study the critical behavior of the Diluted Antiferromagnet in a Field with
the Tethered Monte Carlo formalism. We compute the critical exponents
(including the elusive hyperscaling violations exponent $\theta$). Our results
provide a comprehensive description of the phase transition and clarify the
inconsistencies between previous experimental and theoretical work. To do so,
our method addresses the usual problems of numerical work (large tunneling
barriers and self-averaging violations). | cond-mat_dis-nn |
Unraveling the nature of carrier mediated ferromagnetism in diluted
magnetic semiconductors: After more than a decade of intensive research in the field of diluted
magnetic semiconductors (DMS), the nature and origin of ferromagnetism,
especially in III-V compounds is still controversial. Many questions and open
issues are under intensive debates. Why after so many years of investigations
Mn doped GaAs remains the candidate with the highest Curie temperature among
the broad family of III-V materials doped with transition metal (TM) impurities
? How can one understand that these temperatures are almost two orders of
magnitude larger than that of hole doped (Zn,Mn)Te or (Cd,Mn)Se? Is there any
intrinsic limitation or is there any hope to reach in the dilute regime room
temperature ferromagnetism? How can one explain the proximity of (Ga,Mn)As to
the metal-insulator transition and the change from
Ruderman-Kittel-Kasuya-Yosida (RKKY) couplings in II-VI compounds to double
exchange type in (Ga,Mn)N? In spite of the great success of density functional
theory based studies to provide accurately the critical temperatures in various
compounds, till very lately a theory that provides a coherent picture and
understanding of the underlying physics was still missing. Recently, within a
minimal model it has been possible to show that among the physical parameters,
the key one is the position of the TM acceptor level. By tuning the value of
that parameter, one is able to explain quantitatively both magnetic and
transport properties in a broad family of DMS. We will see that this minimal
model explains in particular the RKKY nature of the exchange in
(Zn,Mn)Te/(Cd,Mn)Te and the double exchange type in (Ga,Mn)N and simultaneously
the reason why (Ga,Mn)As exhibits the highest critical temperature among both
II-VI and III-V DMS. | cond-mat_dis-nn |
Thermodynamics of bidirectional associative memories: In this paper we investigate the equilibrium properties of bidirectional
associative memories (BAMs). Introduced by Kosko in 1988 as a generalization of
the Hopfield model to a bipartite structure, the simplest architecture is
defined by two layers of neurons, with synaptic connections only between units
of different layers: even without internal connections within each layer,
information storage and retrieval are still possible through the reverberation
of neural activities passing from one layer to another. We characterize the
computational capabilities of a stochastic extension of this model in the
thermodynamic limit, by applying rigorous techniques from statistical physics.
A detailed picture of the phase diagram at the replica symmetric level is
provided, both at finite temperature and in the noiseless regimes. Also for the
latter, the critical load is further investigated up to one step of replica
symmetry breaking. An analytical and numerical inspection of the transition
curves (namely critical lines splitting the various modes of operation of the
machine) is carried out as the control parameters - noise, load and asymmetry
between the two layer sizes - are tuned. In particular, with a finite asymmetry
between the two layers, it is shown how the BAM can store information more
efficiently than the Hopfield model by requiring less parameters to encode a
fixed number of patterns. Comparisons are made with numerical simulations of
neural dynamics. Finally, a low-load analysis is carried out to explain the
retrieval mechanism in the BAM by analogy with two interacting Hopfield models.
A potential equivalence with two coupled Restricted Boltmzann Machines is also
discussed. | cond-mat_dis-nn |
Quasicrystalline Bose glass in the absence of disorder and quasidisorder: We study the low-temperature phases of interacting bosons on a
two-dimensional quasicrystalline lattice. By means of numerically exact Path
Integral Monte Carlo simulations, we show that for sufficiently weak
interactions the system is a homogeneous Bose-Einstein condensate, which
develops density modulations for increasing filling factor. The simultaneous
occurrence of sizeable condensate fraction and density modulation can be
interpreted as the analogous, in a quasicrystalline lattice, of supersolid
phases occurring in conventional periodic lattices. For sufficiently large
interaction strength and particle density, global condensation is lost and
quantum exchanges are restricted to specific spatial regions. The emerging
quantum phase is therefore a Bose Glass, which here is stabilized in the
absence of any source of disorder or quasidisorder, purely as a result of the
interplay between quantum effects, particle interactions and quasicrystalline
substrate. This finding clearly indicates that (quasi)disorder is not essential
to observe Bose Glass physics. Our results are of interest for ongoing
experiments on (quasi)disorder-free quasicrystalline lattices. | cond-mat_dis-nn |
Bose-Bose mixtures in a weak-disorder potential: Fluctuations and
superfluidity: We study the properties of a homogeneous dilute Bose-Bose gas in a
weak-disorder potential at zero temperature. By using the perturbation theory,
we calculate the disorder corrections to the condensate density, the equation
of state, the compressibility, and the superfluid density as a function of
density, strength of disorder, and miscibility parameter. It is found that the
disorder potential may lead to modifying the miscibility-immiscibility
condition and a full miscible phase turns out to be impossible in the presence
of the disorder. We show that the intriguing interplay of the disorder and
intra- and interspecies interactions may strongly influence the localization of
each component, the quantum fluctuations, and the compressibility, as well as
the superfluidity of the system. | cond-mat_dis-nn |
Universality of the Wigner time delay distribution for one-dimensional
random potentials: We show that the distribution of the time delay for one-dimensional random
potentials is universal in the high energy or weak disorder limit. Our
analytical results are in excellent agreement with extensive numerical
simulations carried out on samples whose sizes are large compared to the
localisation length (localised regime). The case of small samples is also
discussed (ballistic regime). We provide a physical argument which explains in
a quantitative way the origin of the exponential divergence of the moments. The
occurence of a log-normal tail for finite size systems is analysed. Finally, we
present exact results in the low energy limit which clearly show a departure
from the universal behaviour. | cond-mat_dis-nn |
Interaction-enhanced integer quantum Hall effect in disordered systems: We study transport properties and topological phase transition in
two-dimensional interacting disordered systems. Within dynamical mean-field
theory, we derive the Hall conductance, which is quantized and serves as a
topological invariant for insulators, even when the energy gap is closed by
localized states. In the spinful Harper-Hofstadter-Hatsugai model, in the
trivial insulator regime, we find that the repulsive on-site interaction can
assist weak disorder to induce the integer quantum Hall effect, while in the
topologically non-trivial regime, it impedes Anderson localization. Generally,
the interaction broadens the regime of the topological phase in the disordered
system. | cond-mat_dis-nn |
Random matrices with row constraints and eigenvalue distributions of
graph Laplacians: Symmetric matrices with zero row sums occur in many theoretical settings and
in real-life applications. When the offdiagonal elements of such matrices are
i.i.d. random variables and the matrices are large, the eigenvalue
distributions converge to a peculiar universal curve
$p_{\mathrm{zrs}}(\lambda)$ that looks like a cross between the Wigner
semicircle and a Gaussian distribution. An analytic theory for this curve,
originally due to Fyodorov, can be developed using supersymmetry-based
techniques.
We extend these derivations to the case of sparse matrices, including the
important case of graph Laplacians for large random graphs with $N$ vertices of
mean degree $c$. In the regime $1\ll c\ll N$, the eigenvalue distribution of
the ordinary graph Laplacian (diffusion with a fixed transition rate per edge)
tends to a shifted and scaled version of $p_{\mathrm{zrs}}(\lambda)$, centered
at $c$ with width $\sim\sqrt{c}$. At smaller $c$, this curve receives
corrections in powers of $1/\sqrt{c}$ accurately captured by our theory. For
the normalized graph Laplacian (diffusion with a fixed transition rate per
vertex), the large $c$ limit is a shifted and scaled Wigner semicircle, again
with corrections captured by our analysis. | cond-mat_dis-nn |
Note: Effect of localization on mean-field density of state near jamming: We discuss the effects of the localized modes on the density of state
$D(\omega)$ by introducing the probability distribution function of the
proximity to the marginal stability. Our theoretical treatment reproduces the
numerical results in finite dimensions near the jamming point., in particular,
successfully captures the novel $D(\omega)\sim \omega^4$ scaling including its
pressure dependence of the pre-factor. | cond-mat_dis-nn |
Phase Transition in the Random Anisotropy Model: The influence of a local anisotropy of random orientation on a ferromagnetic
phase transition is studied for two cases of anisotropy axis distribution. To
this end a model of a random anisotropy magnet is analyzed by means of the
field theoretical renormalization group approach in two loop approximation
refined by a resummation of the asymptotic series. The one-loop result of
Aharony indicating the absence of a second-order phase transition for an
isotropic distribution of random anisotropy axis at space dimension $d<4$ is
corroborated. For a cubic distribution the accessible stable fixed point leads
to disordered Ising-like critical exponents. | cond-mat_dis-nn |
Atomistic simulation of nearly defect-free models of amorphous silicon:
An information-based approach: We present an information-based total-energy optimization method to produce
nearly defect-free structural models of amorphous silicon. Using geometrical,
structural and topological information from disordered tetrahedral networks, we
have shown that it is possible to generate structural configurations of
amorphous silicon, which are superior than the models obtained from
conventional reverse Monte Carlo and molecular-dynamics simulations. The new
data-driven hybrid approach presented here is capable of producing atomistic
models with structural and electronic properties which are on a par with those
obtained from the modified Wooten-Winer-Weaire (WWW) models of amorphous
silicon. Structural, electronic and thermodynamic properties of the hybrid
models are compared with the best dynamical models obtained from using
machine-intelligence-based potentials and efficient classical
molecular-dynamics simulations, reported in the recent literature. We have
shown that, together with the WWW models, our hybrid models represent one of
the best structural models so far produced by total-energy-based Monte Carlo
methods in conjunction with experimental diffraction data and a few structural
constraints. | cond-mat_dis-nn |
Localization crossover and subdiffusive transport in a classical
facilitated network model of a disordered, interacting quantum spin chain: We consider the random-field Heisenberg model, a paradigmatic model for
many-body localization (MBL), and add a Markovian dephasing bath coupled to the
Anderson orbitals of the model's non-interacting limit. We map this system to a
classical facilitated hopping model that is computationally tractable for large
system sizes, and investigate its dynamics. The classical model exhibits a
robust crossover between an ergodic (thermal) phase and a frozen (localized)
phase. The frozen phase is destabilized by thermal subregions (bubbles), which
thermalize surrounding sites by providing a fluctuating interaction energy and
so enable off-resonance particle transport. Investigating steady state
transport, we observe that the interplay between thermal and frozen bubbles
leads to a clear transition between diffusive and subdiffusive regimes. This
phenomenology both describes the MBL system coupled to a bath, and provides a
classical analogue for the many-body localization transition in the
corresponding quantum model, in that the classical model displays long local
memory times. It also highlights the importance of the details of the bath
coupling in studies of MBL systems coupled to thermal environments. | cond-mat_dis-nn |
Spatial Structure of the Internet Traffic: The Internet infrastructure is not virtual: its distribution is dictated by
social, geographical, economical, or political constraints. However, the
infrastructure's design does not determine entirely the information traffic and
different sources of complexity such as the intrinsic heterogeneity of the
network or human practices have to be taken into account. In order to manage
the Internet expansion, plan new connections or optimize the existing ones, it
is thus critical to understand correlations between emergent global statistical
patterns of Internet activity and human factors. We analyze data from the
French national `Renater' network which has about two millions users and which
consists in about 30 interconnected routers located in different regions of
France and we report the following results. The Internet flow is strongly
localized: most of the traffic takes place on a `spanning' network connecting a
small number of routers which can be classified either as `active centers'
looking for information or `databases' providing information. We also show that
the Internet activity of a region increases with the number of published papers
by laboratories of that region, demonstrating the positive impact of the Web on
scientific activity and illustrating quantitatively the adage `the more you
read, the more you write'. | cond-mat_dis-nn |
Anderson localization in Bose-Einstein condensates: The understanding of disordered quantum systems is still far from being
complete, despite many decades of research on a variety of physical systems. In
this review we discuss how Bose-Einstein condensates of ultracold atoms in
disordered potentials have opened a new window for studying fundamental
phenomena related to disorder. In particular, we point our attention to recent
experimental studies on Anderson localization and on the interplay of disorder
and weak interactions. These realize a very promising starting point for a
deeper understanding of the complex behaviour of interacting, disordered
systems. | cond-mat_dis-nn |
q-Random Matrix Ensembles: Theory of Random Matrix Ensembles have proven to be a useful tool in the
study of the statistical distribution of energy or transmission levels of a
wide variety of physical systems. We give an overview of certain
q-generalizations of the Random Matrix Ensembles, which were first introduced
in connection with the statistical description of disordered quantum
conductors. | cond-mat_dis-nn |
Spectra of Modular and Small-World Matrices: We compute spectra of symmetric random matrices describing graphs with
general modular structure and arbitrary inter- and intra-module degree
distributions, subject only to the constraint of finite mean connectivities. We
also evaluate spectra of a certain class of small-world matrices generated from
random graphs by introducing short-cuts via additional random connectivity
components. Both adjacency matrices and the associated graph Laplacians are
investigated. For the Laplacians, we find Lifshitz type singular behaviour of
the spectral density in a localised region of small $|\lambda|$ values. In the
case of modular networks, we can identify contributions local densities of
state from individual modules. For small-world networks, we find that the
introduction of short cuts can lead to the creation of satellite bands outside
the central band of extended states, exhibiting only localised states in the
band-gaps. Results for the ensemble in the thermodynamic limit are in excellent
agreement with those obtained via a cavity approach for large finite single
instances, and with direct diagonalisation results. | cond-mat_dis-nn |
Current Redistribution in Resistor Networks: Fat-Tail Statistics in
Regular and Small-World Networks: The redistribution of electrical currents in resistor networks after
single-bond failures is analyzed in terms of current-redistribution factors
that are shown to depend only on the topology of the network and on the values
of the bond resistances. We investigate the properties of these
current-redistribution factors for regular network topologies (e.g.
$d$-dimensional hypercubic lattices) as well as for small-world networks. In
particular, we find that the statistics of the current redistribution factors
exhibits a fat-tail behavior, which reflects the long-range nature of the
current redistribution as determined by Kirchhoff's circuit laws. | cond-mat_dis-nn |
Study of the de Almeida-Thouless line using power-law diluted
one-dimensional Ising spin glasses: We test for the existence of a spin-glass phase transition, the de
Almeida-Thouless line, in an externally-applied (random) magnetic field by
performing Monte Carlo simulations on a power-law diluted one-dimensional Ising
spin glass for very large system sizes. We find that an Almeida-Thouless line
only occurs in the mean field regime, which corresponds, for a short-range spin
glass, to dimension d larger than 6. | cond-mat_dis-nn |
Interface Energy in the Edwards-Anderson model: We numerically investigate the spin glass energy interface problem in three
dimensions. We analyze the energy cost of changing the overlap from -1 to +1 at
one boundary of two coupled systems (in the other boundary the overlap is kept
fixed to +1). We implement a parallel tempering algorithm that simulate finite
temperature systems and work with both cubic lattices and parallelepiped with
fixed aspect ratio. We find results consistent with a lower critical dimension
$D_c=2.5$. The results show a good agreement with the mean field theory
predictions. | cond-mat_dis-nn |
Low-rank combinatorial optimization and statistical learning by spatial
photonic Ising machine: The spatial photonic Ising machine (SPIM) [D. Pierangeli et al., Phys. Rev.
Lett. 122, 213902 (2019)] is a promising optical architecture utilizing spatial
light modulation for solving large-scale combinatorial optimization problems
efficiently. The primitive version of the SPIM, however, can accommodate Ising
problems with only rank-one interaction matrices. In this Letter, we propose a
new computing model for the SPIM that can accommodate any Ising problem without
changing its optical implementation. The proposed model is particularly
efficient for Ising problems with low-rank interaction matrices, such as
knapsack problems. Moreover, it acquires the learning ability of Boltzmann
machines. We demonstrate that learning, classification, and sampling of the
MNIST handwritten digit images are achieved efficiently using the model with
low-rank interactions. Thus, the proposed model exhibits higher practical
applicability to various problems of combinatorial optimization and statistical
learning, without losing the scalability inherent in the SPIM architecture. | cond-mat_dis-nn |
Statistics of the Mesoscopic Field: We find in measurements of microwave transmission through quasi-1D dielectric
samples for both diffusive and localized waves that the field normalized by the
square root of the spatially averaged flux in a given sample configuration is a
Gaussian random process with position, polarization, frequency, and time. As a
result, the probability distribution of the field in the random ensemble is a
mixture of Gaussian functions weighted by the distribution of total
transmission, while its correlation function is a product of correlators of the
Gaussian field and the square root of the total transmission. | cond-mat_dis-nn |
Slow conductance relaxations; Distinguishing the Electron Glass from
extrinsic mechanisms: Slow conductance relaxations are observable in a many condensed matter
systems. These are sometimes described as manifestations of a glassy phase. The
underlying mechanisms responsible for the slow dynamics are often due to
structural changes which modify the potential landscape experienced by the
charge-carriers and thus are reflected in the conductance. Sluggish conductance
dynamics may however originate from the interplay between electron-electron
interactions and quenched disorder. Examples for both scenarios and the
experimental features that should help to distinguish between them are shown
and discussed. In particular, it is suggested that the `memory-dip' observable
through field-effect measurements is a characteristic signature of the inherent
electron-glass provided it obeys certain conditions. | cond-mat_dis-nn |
Influence of synaptic depression on memory storage capacity: Synaptic efficacy between neurons is known to change within a short time
scale dynamically. Neurophysiological experiments show that high-frequency
presynaptic inputs decrease synaptic efficacy between neurons. This phenomenon
is called synaptic depression, a short term synaptic plasticity. Many
researchers have investigated how the synaptic depression affects the memory
storage capacity. However, the noise has not been taken into consideration in
their analysis. By introducing "temperature", which controls the level of the
noise, into an update rule of neurons, we investigate the effects of synaptic
depression on the memory storage capacity in the presence of the noise. We
analytically compute the storage capacity by using a statistical mechanics
technique called Self Consistent Signal to Noise Analysis (SCSNA). We find that
the synaptic depression decreases the storage capacity in the case of finite
temperature in contrast to the case of the low temperature limit, where the
storage capacity does not change. | cond-mat_dis-nn |
Simulated annealing, optimization, searching for ground states: The chapter starts with a historical summary of first attempts to optimize
the spin glass Hamiltonian, comparing it to recent results on searching largest
cliques in random graphs. Exact algorithms to find ground states in generic
spin glass models are then explored in Section 1.2, while Section 1.3 is
dedicated to the bidimensional case where polynomial algorithms exist and allow
for the study of much larger systems. Finally Section 1.4 presents a summary of
results for the assignment problem where the finite size corrections for the
ground state can be studied in great detail. | cond-mat_dis-nn |
Sequence Nets: We study a new class of networks, generated by sequences of letters taken
from a finite alphabet consisting of $m$ letters (corresponding to $m$ types of
nodes) and a fixed set of connectivity rules. Recently, it was shown how a
binary alphabet might generate threshold nets in a similar fashion [Hagberg et
al., Phys. Rev. E 74, 056116 (2006)]. Just like threshold nets, sequence nets
in general possess a modular structure reminiscent of everyday life nets, and
are easy to handle analytically (i.e., calculate degree distribution, shortest
paths, betweenness centrality, etc.). Exploiting symmetry, we make a full
classification of two- and three-letter sequence nets, discovering two new
classes of two-letter sequence nets. The new sequence nets retain many of the
desirable analytical properties of threshold nets while yielding richer
possibilities for the modeling of everyday life complex networks more
faithfully. | cond-mat_dis-nn |
On the critical behavior of the Susceptible-Infected-Recovered (SIR)
model on a square lattice: By means of numerical simulations and epidemic analysis, the transition point
of the stochastic, asynchronous Susceptible-Infected-Recovered (SIR) model on a
square lattice is found to be c_0=0.1765005(10), where c is the probability a
chosen infected site spontaneously recovers rather than tries to infect one
neighbor. This point corresponds to an infection/recovery rate of lambda_c =
(1-c_0)/c_0 = 4.66571(3) and a net transmissibility of (1-c_0)/(1 + 3 c_0) =
0.538410(2), which falls between the rigorous bounds of the site and bond
thresholds. The critical behavior of the model is consistent with the 2-d
percolation universality class, but local growth probabilities differ from
those of dynamic percolation cluster growth, as is demonstrated explicitly. | cond-mat_dis-nn |
Slow Nonthermalizing Dynamics in a Quantum Spin Glass: Spin glasses and many-body localization (MBL) are prime examples of
ergodicity breaking, yet their physical origin is quite different: the former
phase arises due to rugged classical energy landscape, while the latter is a
quantum-interference effect. Here we study quantum dynamics of an isolated 1d
spin-glass under application of a transverse field. At high energy densities,
the system is ergodic, relaxing via resonance avalanche mechanism, that is also
responsible for the destruction of MBL in non-glassy systems with power-law
interactions. At low energy densities, the interaction-induced fields obtain a
power-law soft gap, making the resonance avalanche mechanism inefficient. This
leads to the persistence of the spin-glass order, as demonstrated by resonance
analysis and by numerical studies. A small fraction of resonant spins forms a
thermalizing system with long-range entanglement, making this regime distinct
from the conventional MBL. The model considered can be realized in systems of
trapped ions, opening the door to investigating slow quantum dynamics induced
by glassiness. | cond-mat_dis-nn |
Universal crossover from ground state to excited-state quantum
criticality: We study the nonequilibrium properties of a nonergodic random quantum chain
in which highly excited eigenstates exhibit critical properties usually
associated with quantum critical ground states. The ground state and excited
states of this system belong to different universality classes, characterized
by infinite-randomness quantum critical behavior. Using strong-disorder
renormalization group techniques, we show that the crossover between the zero
and finite energy density regimes is universal. We analytically derive a flow
equation describing the unitary dynamics of this isolated system at finite
energy density from which we obtain universal scaling functions along the
crossover. | cond-mat_dis-nn |
Breakdown of Dynamical Scale Invariance in the Coarsening of Fractal
Clusters: We extend a previous analysis [PRL {\bf 80}, 4693 (1998)] of breakdown of
dynamical scale invariance in the coarsening of two-dimensional DLAs
(diffusion-limited aggregates) as described by the Cahn-Hilliard equation.
Existence of a second dynamical length scale, predicted earlier, is
established. Having measured the "solute mass" outside the cluster versus time,
we obtain a third dynamical exponent. An auxiliary problem of the dynamics of a
slender bar (that acquires a dumbbell shape) is considered. A simple scenario
of coarsening of fractal clusters with branching structure is suggested that
employs the dumbbell dynamics results. This scenario involves two dynamical
length scales: the characteristic width and length of the cluster branches. The
predicted dynamical exponents depend on the (presumably invariant) fractal
dimension of the cluster skeleton. In addition, a robust theoretical estimate
for the third dynamical exponent is obtained. Exponents found numerically are
in reasonable agreement with these predictions. | cond-mat_dis-nn |
Real space information from Fluctuation electron microscopy:
Applications to amorphous silicon: Ideal models of complex materials must satisfy all available information
about the system. Generally, this information consists of experimental data,
information implicit to sophisticated interatomic interactions and potentially
other {\it a priori} information. By jointly imposing first-principles or
tight-binding information in conjunction with experimental data, we have
developed a method: Experimentally Constrained Molecular Relaxation (ECMR) that
uses {\it all} of the information available. We apply the method to model
medium range order in amorphous silicon using Fluctuation Electron microscopy
(FEM) data as experimental information. The paracrystalline model of medium
range order is examined, and a new model based on voids in amorphous silicon is
proposed. Our work suggests that films of amorphous silicon showing medium
range order (in FEM experiments) can be accurately represented by a continuous
random network model with inhomogeneities consisting of ordered grains and
voids dispersed in the network. | cond-mat_dis-nn |
Network Synchronization, Diffusion, and the Paradox of Heterogeneity: Many complex networks display strong heterogeneity in the degree
(connectivity) distribution. Heterogeneity in the degree distribution often
reduces the average distance between nodes but, paradoxically, may suppress
synchronization in networks of oscillators coupled symmetrically with uniform
coupling strength. Here we offer a solution to this apparent paradox. Our
analysis is partially based on the identification of a diffusive process
underlying the communication between oscillators and reveals a striking
relation between this process and the condition for the linear stability of the
synchronized states. We show that, for a given degree distribution, the maximum
synchronizability is achieved when the network of couplings is weighted and
directed, and the overall cost involved in the couplings is minimum. This
enhanced synchronizability is solely determined by the mean degree and does not
depend on the degree distribution and system size. Numerical verification of
the main results is provided for representative classes of small-world and
scale-free networks. | cond-mat_dis-nn |
Slow conductance relaxations; Distinguishing the Electron Glass from
extrinsic mechanisms: Slow conductance relaxations are observable in a many condensed matter
systems. These are sometimes described as manifestations of a glassy phase. The
underlying mechanisms responsible for the slow dynamics are often due to
structural changes which modify the potential landscape experienced by the
charge-carriers and thus are reflected in the conductance. Sluggish conductance
dynamics may however originate from the interplay between electron-electron
interactions and quenched disorder. Examples for both scenarios and the
experimental features that should help to distinguish between them are shown
and discussed. In particular, it is suggested that the `memory-dip' observable
through field-effect measurements is a characteristic signature of the inherent
electron-glass provided it obeys certain conditions. | cond-mat_dis-nn |
Free energy fluctuations and chaos in the Sherrington-Kirkpatrick model: The sample-to-sample fluctuations Delta F_N of the free energy in the
Sherrington-Kirkpatrick model are shown rigorously to be related to bond chaos.
Via this connection, the fluctuations become analytically accessible by replica
methods. The replica calculation for bond chaos shows that the exponent mu
governing the growth of the fluctuations with system size N, i.e. Delta F_N
N^mu, is bounded by mu <= 1/4. | cond-mat_dis-nn |
Network synchronization: Optimal and Pessimal Scale-Free Topologies: By employing a recently introduced optimization algorithm we explicitely
design optimally synchronizable (unweighted) networks for any given scale-free
degree distribution. We explore how the optimization process affects
degree-degree correlations and observe a generic tendency towards
disassortativity. Still, we show that there is not a one-to-one correspondence
between synchronizability and disassortativity. On the other hand, we study the
nature of optimally un-synchronizable networks, that is, networks whose
topology minimizes the range of stability of the synchronous state. The
resulting ``pessimal networks'' turn out to have a highly assortative
string-like structure. We also derive a rigorous lower bound for the Laplacian
eigenvalue ratio controlling synchronizability, which helps understanding the
impact of degree correlations on network synchronizability. | cond-mat_dis-nn |
Soft-margin classification of object manifolds: A neural population responding to multiple appearances of a single object
defines a manifold in the neural response space. The ability to classify such
manifolds is of interest, as object recognition and other computational tasks
require a response that is insensitive to variability within a manifold. Linear
classification of object manifolds was previously studied for max-margin
classifiers. Soft-margin classifiers are a larger class of algorithms and
provide an additional regularization parameter used in applications to optimize
performance outside the training set by balancing between making fewer training
errors and learning more robust classifiers. Here we develop a mean-field
theory describing the behavior of soft-margin classifiers applied to object
manifolds. Analyzing manifolds with increasing complexity, from points through
spheres to general manifolds, a mean-field theory describes the expected value
of the linear classifier's norm, as well as the distribution of fields and
slack variables. By analyzing the robustness of the learned classification to
noise, we can predict the probability of classification errors and their
dependence on regularization, demonstrating a finite optimal choice. The theory
describes a previously unknown phase transition, corresponding to the
disappearance of a non-trivial solution, thus providing a soft version of the
well-known classification capacity of max-margin classifiers. | cond-mat_dis-nn |
Localization of vibrational modes in high-entropy oxides: The recently-discovered high-entropy oxides offer a paradoxical combination
of crystalline arrangement and high disorder. They differ qualitatively from
established paradigms for disordered solids such as glasses and alloys. In
these latter systems, it is well known that disorder induces localized
vibrational excitations. In this article, we explore the possibility of
disorder-induced localization in (MgCoCuNiZn)O, the prototypical high-entropy
oxide with rock-salt structure. To describe phononic excitations, we model the
interatomic potentials for the cation-oxygen interactions by fitting to the
physical properties of the parent binary oxides. We validate our model against
the experimentally determined crystal structure, bond lengths, and optical
conductivity. The resulting phonon spectrum shows wave-like propagating modes
at low energies and localized modes at high energies. Localization is reflected
in signatures such as participation ratio and correlation amplitude. Finally,
we explore the possibility of increased mass disorder in the oxygen sublattice.
Admixing sulphur or tellurium atoms with oxygen enhances localization. It even
leads to localized modes in the middle of the spectrum. Our results suggest
that high-entropy oxides are a promising platform to study Anderson
localization of phonons. | cond-mat_dis-nn |
Distribution of velocities in an avalanche, and related quantities:
Theory and numerical verification: We study several probability distributions relevant to the avalanche dynamics
of elastic interfaces driven on a random substrate: The distribution of size,
duration, lateral extension or area, as well as velocities. Results from the
functional renormalization group and scaling relations involving two
independent exponents, roughness $\zeta$, and dynamics $z$, are confronted to
high-precision numerical simulations of an elastic line with short-range
elasticity, i.e. of internal dimension $d=1$. The latter are based on a novel
stochastic algorithm which generates its disorder on the fly. Its precision
grows linearly in the time-discretization step, and it is parallelizable. Our
results show good agreement between theory and numerics, both for the critical
exponents as for the scaling functions. In particular, the prediction ${\sf a}
= 2 - \frac{2}{d+ \zeta - z}$ for the velocity exponent is confirmed with good
accuracy. | cond-mat_dis-nn |
Localization of weakly disordered flat band states: Certain tight binding lattices host macroscopically degenerate flat spectral
bands. Their origin is rooted in local symmetries of the lattice, with
destructive interference leading to the existence of compact localized
eigenstates. We study the robustness of this localization to disorder in
different classes of flat band lattices in one and two dimensions. Depending on
the flat band class, the flat band states can either be robust, preserving
their strong localization for weak disorder W, or they are destroyed and
acquire large localization lengths $\xi$ that diverge with a variety of
unconventional exponents $\nu$, $\xi \sim 1/W^{\nu}$. | cond-mat_dis-nn |
Phase Ordering and Onset of Collective Behavior in Chaotic Coupled Map
Lattices: The phase ordering properties of lattices of band-chaotic maps coupled
diffusively with some coupling strength $g$ are studied in order to determine
the limit value $g_e$ beyond which multistability disappears and non-trivial
collective behavior is observed. The persistence of equivalent discrete spin
variables and the characteristic length of the patterns observed scale
algebraically with time during phase ordering. The associated exponents vary
continuously with $g$ but remain proportional to each other, with a ratio close
to that of the time-dependent Ginzburg-Landau equation. The corresponding
individual values seem to be recovered in the space-continuous limit. | cond-mat_dis-nn |
Statistical Mechanical Development of a Sparse Bayesian Classifier: The demand for extracting rules from high dimensional real world data is
increasing in various fields. However, the possible redundancy of such data
sometimes makes it difficult to obtain a good generalization ability for novel
samples. To resolve this problem, we provide a scheme that reduces the
effective dimensions of data by pruning redundant components for bicategorical
classification based on the Bayesian framework. First, the potential of the
proposed method is confirmed in ideal situations using the replica method.
Unfortunately, performing the scheme exactly is computationally difficult. So,
we next develop a tractable approximation algorithm, which turns out to offer
nearly optimal performance in ideal cases when the system size is large.
Finally, the efficacy of the developed classifier is experimentally examined
for a real world problem of colon cancer classification, which shows that the
developed method can be practically useful. | cond-mat_dis-nn |
Critical Line in Random Threshold Networks with Inhomogeneous Thresholds: We calculate analytically the critical connectivity $K_c$ of Random Threshold
Networks (RTN) for homogeneous and inhomogeneous thresholds, and confirm the
results by numerical simulations. We find a super-linear increase of $K_c$ with
the (average) absolute threshold $|h|$, which approaches $K_c(|h|) \sim
h^2/(2\ln{|h|})$ for large $|h|$, and show that this asymptotic scaling is
universal for RTN with Poissonian distributed connectivity and threshold
distributions with a variance that grows slower than $h^2$. Interestingly, we
find that inhomogeneous distribution of thresholds leads to increased
propagation of perturbations for sparsely connected networks, while for densely
connected networks damage is reduced; the cross-over point yields a novel,
characteristic connectivity $K_d$, that has no counterpart in Boolean networks.
Last, local correlations between node thresholds and in-degree are introduced.
Here, numerical simulations show that even weak (anti-)correlations can lead to
a transition from ordered to chaotic dynamics, and vice versa. It is shown that
the naive mean-field assumption typical for the annealed approximation leads to
false predictions in this case, since correlations between thresholds and
out-degree that emerge as a side-effect strongly modify damage propagation
behavior. | cond-mat_dis-nn |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.