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6,400 | A Field Theory for Finite Dimensional Site Disordered Spin Systems | cond-mat.dis-nn | We present a new field theoretic approach for finite dimensional site
disordered spin systems by introducing the notion of grand canonical disorder,
where the number of spins in the system is random but quenched. We analyze this
field theory using the variational replica formalism. For a variety of
interactions we find... | physics |
6,401 | Hierarchical Diffusion, Aging and Multifractality | cond-mat.dis-nn | We study toy aging processes in hierarchically decomposed phase spaces where
the equilibrium probability distributions are multifractal. We found that the
an auto-correlation function, survival-return probability, shows crossover
behavior from a power law $t^{-x}$ in the quasi-equilibrium regime ($t\ll\tw$)
to another ... | physics |
6,402 | Retrieval Phase Diagrams of Non-monotonic Hopfield Networks | cond-mat.dis-nn | We investigate the retrieval phase diagrams of an asynchronous
fully-connected attractor network with non-monotonic transfer function by means
of a mean-field approximation. We find for the noiseless zero-temperature case
that this non-monotonic Hopfield network can store more patterns than a network
with monotonic tra... | physics |
6,403 | A Single Slice 2d Anderson Model at Weak Disorder | cond-mat.dis-nn | We introduce a matrix-operator formulation of the Anderson model in d=2. In a
single slice, we can then derive an analogy between our model and a standard
random matrices problem. This enables us to construct and control the Green
function in one slice, which is an important prerequisite to a full multi-scale
study of ... | physics |
6,404 | Site Disordered Spin Systems in the Gaussian Variational Approximation | cond-mat.dis-nn | We define a replica field theory describing finite dimensional site
disordered spin systems by introducing the notion of grand canonical disorder,
where the number of spins in the system is random but quenched. A general
analysis of this field theory is made using the Gaussian variational or Hartree
Fock method, and il... | physics |
6,405 | Statistical mechanics of the random K-SAT model | cond-mat.dis-nn | The Random K-Satisfiability Problem, consisting in verifying the existence of
an assignment of N Boolean variables that satisfy a set of M=alpha N random
logical clauses containing K variables each, is studied using the replica
symmetric framework of diluted disordered systems. We present an exact
iterative scheme for ... | physics |
6,406 | Hopfield models as generalized random mean field models | cond-mat.dis-nn | We give a comprehensive self-contained review on the rigorous analysis of the
thermodynamics of a class of random spin systems of mean field type whose most
prominent example is the Hopfield model. We focus on the low temperature phase
and the analysis of the Gibbs measures with large deviation techniques. There
is a v... | physics |
6,407 | Multifractality and percolation in the coupling space of perceptrons | cond-mat.dis-nn | The coupling space of perceptrons with continuous as well as with binary
weights gets partitioned into a disordered multifractal by a set of $p=\gamma
N$ random input patterns. The multifractal spectrum $f(\alpha)$ can be
calculated analytically using the replica formalism. The storage capacity and
the generalization b... | physics |
6,408 | Ground state properties of solid-on-solid models with disordered substrates | cond-mat.dis-nn | We study the glassy super-rough phase of a class of solid-on-solid models
with a disordered substrate in the limit of vanishing temperature by means of
exact ground states, which we determine with a newly developed minimum cost
flow algorithm. Results for the height-height correlation function are compared
with analyti... | physics |
6,409 | An Experimentally Realizable Weiss Model for Disorder-Free Glassiness | cond-mat.dis-nn | We summarize recent work on a frustrated periodic long-range Josephson array
in a parameter regime where its dynamical behavior is identical to that of the
$p=4$ disordered spherical model. We also discuss the physical requirements
imposed by the theory on the experimental realization of this superconducting
network. | physics |
6,410 | On the Decay of Localized Vibrational States in Glasses: a one-dimensional example | cond-mat.dis-nn | The interaction between three localized vibrational modes is shown to be as
relevant for the lifetimes of localized modes as the interaction involving two
localized and one extended, and one localized and two extended modes. This
contrasts with previous views. I support my arguments by a numerical study of a
strongly d... | physics |
6,411 | Stationary Localized States Due to a Nonlinear Dimeric Impurity Embedded in a Perfect 1-D Chain | cond-mat.dis-nn | The formation of Stationary Localized states due to a nonlinear dimeric
impurity embedded in a perfect 1-d chain is studied here using the appropriate
Discrete Nonlinear Schr$\ddot{o}$dinger Equation. Furthermore, the nonlinearity
has the form, $\chi |C|^\sigma$ where $C$ is the complex amplitude. A proper
ansatz for t... | physics |
6,412 | Storage capacity of correlated perceptrons | cond-mat.dis-nn | We consider an ensemble of $K$ single-layer perceptrons exposed to random
inputs and investigate the conditions under which the couplings of these
perceptrons can be chosen such that prescribed correlations between the outputs
occur. A general formalism is introduced using a multi-perceptron costfunction
that allows to... | physics |
6,413 | Replica Symmetry Breaking and the Kuhn-Tucker Cavity Method in simple and multilayer Perceptrons | cond-mat.dis-nn | Within a Kuhn-Tucker cavity method introduced in a former paper, we study
optimal stability learning for situations, where in the replica formalism the
replica symmetry may be broken, namely
(i) the case of a simple perceptron above the critical loading, and
(ii) the case of two-layer AND-perceptrons, if one learns... | physics |
6,414 | The Lyapunov Spectrum of a Continuous Product of Random Matrices | cond-mat.dis-nn | We expose a functional integration method for the averaging of continuous
products $\hat{P}_t$ of $N\times N$ random matrices. As an application, we
compute exactly the statistics of the Lyapunov spectrum of $\hat{P}_t$. This
problem is relevant to the study of the statistical properties of various
disordered physical ... | physics |
6,415 | Transport properties of one-dimensional Kronig-Penney models with correlated disorder | cond-mat.dis-nn | Transport properties of one-dimensional Kronig-Penney models with binary
correlated disorder are analyzed using an approach based on classical
Hamiltonian maps. In this method, extended states correspond to bound
trajectories in the phase space of a parametrically excited linear oscillator,
while the on site-potential ... | physics |
6,416 | Vector breaking of replica symmetry in some low temperature disordered systems | cond-mat.dis-nn | We present a new method to study disordered systems in the low temperature
limit. The method uses the replicated Hamiltonian. It studies the saddle points
of this Hamiltonian and shows how the various saddle point contributions can be
resummed in order to obtain the scaling behaviour at low temperatures. In a
large cla... | physics |
6,417 | Solving the Schroedinger equation for the Sherrington-Kirkpatrick model in a transverse field | cond-mat.dis-nn | By numerically solving the Schr\"oedinger equation for small sizes we
investigate the quantum critical point of the infinite-range Ising spin glass
in a transverse field at zero temperature. Despite its simplicity the method
yields accurate information on the value of the critical field and critical
exponents. We obtai... | physics |
6,418 | Classical and Quantum Behavior in Mean-Field Glassy Systems | cond-mat.dis-nn | In this talk I review some recent developments which shed light on the main
connections between structural glasses and mean-field spin glass models with a
discontinuous transition. I also discuss the role of quantum fluctuations on
the dynamical instability found in mean-field spin glasses with a discontinuous
transiti... | physics |
6,419 | Aging and effective temperatures in the low temperature mode-coupling equations | cond-mat.dis-nn | The low-temperature generalization of the mode-coupling equations corresponds
to the dynamics of mean-field disordered models in the glassy phase. The system
never achieves equilibrium, preserving the memory of the time elapsed after the
quench throughout its evolution. A concept of effective temperature can be made
qu... | physics |
6,420 | Disordered systems and the metal-insulator Transition: A super universality class | cond-mat.dis-nn | The critical behaviour of three-dimensional disordered systems is
investigated by analysing the spectral fluctuations of the energy spectrum. Our
results suggest that the initial symmetries (orthogonal, unitary and
symplectic) are broken by the disorder at the critical point. The critical
behaviour, determinedby the sy... | physics |
6,421 | Structure of metastable states in spin glasses by means of a three replica potential | cond-mat.dis-nn | We introduce a three replica potential useful to examine the structure of
metastables states above the static transition temperature, in the spherical
p-spin model. Studying the minima of the potential we are able to find which is
the distance between the nearest equilibrium and local equilibrium states,
obtaining in t... | physics |
6,422 | On the Stability of the Mean-Field Glass Broken Phase under Non-Hamiltonian Perturbations | cond-mat.dis-nn | We study the dynamics of the SK model modified by a small non-hamiltonian
perturbation. We study aging, and we find that on the time scales investigated
by our numerical simulations it survives a small perturbation (and is destroyed
by a large one). If we assume we are observing a transient behavior the scaling
of corr... | physics |
6,423 | Static Critical Behavior of the Spin-Freezing Transition in the Geometrically Frustrated Pyrochlore Antiferromagnet Y2Mo2O7 | cond-mat.dis-nn | Some frustrated pyrochlore antiferromagnets, such as Y2Mo2O7, show a
spin-freezing transition and magnetic irreversibilities below a temperature Tf
similar to what is observed nonlinear magnetization measurements on Y2Mo2O7
that provide strong evidence that there is an underlying thermodynamic phase
transition at Tf, w... | physics |
6,424 | Learning by dilution in a Neural Network | cond-mat.dis-nn | A perceptron with N random weights can store of the order of N patterns by
removing a fraction of the weights without changing their strengths. The
critical storage capacity as a function of the concentration of the remaining
bonds for random outputs and for outputs given by a teacher perceptron is
calculated. A simple... | physics |
6,425 | Relaxational Modes and Aging in the Glauber Dynamics of the Sherrington-Kirkpatrick Model | cond-mat.dis-nn | The relaxational modes and aging of the Glauber dynamics of the mean-field
spin-glass model, SK model, are studied by a numerical diagonalization
technique and Monte Carlo simulations. We found that the aging process of the
model is understood as hierarchical growth of quasi-equilibrium domain in the
phase-space. | physics |
6,426 | Ginzburg-Landau theory of the cluster glass phase | cond-mat.dis-nn | On the basis of a recent field theory for site-disordered spin glasses a
Ginzburg-Landau free energy is proposed to describe the low temperatures glassy
phase(s) of site-disordered magnets. The prefactors of the cubic and dominant
quartic terms change gradually along the transition line in the
concentration-temperature... | physics |
6,427 | Domain wall roughening in disordered media: From local spin dynamics to a continuum description of the interface | cond-mat.dis-nn | We study the kinetic roughening of a driven domain wall between spin-up and
spin-down domains for a model with non-conserved order parameter and quenched
disorder. To understand the scaling behavior of this interface we construct an
equation of motion and study it theoretically. | physics |
6,428 | No enhancement of the localization length for two interacting particles in a random potential | cond-mat.dis-nn | We study two interacting particles in a random potential chain by means of
the transfer matrix method. The dependence of the two-particle localization
length $\lambda_2$ on disorder and interaction strength is investigated. Our
results demonstrate that the recently proposed enhancement of $\lambda_2$ as
compared to the... | physics |
6,429 | Random walk on disordered networks | cond-mat.dis-nn | Random walks are studied on disordered cellular networks in 2-and
3-dimensional spaces with arbitrary curvature. The coefficients of the
evolution equation are calculated in term of the structural properties of the
cellular system. The effects of disorder and space-curvature on the diffusion
phenomena are investigated.... | physics |
6,430 | Aging Processes within One `Pure State' of the SK Model | cond-mat.dis-nn | Monte Carlo simulations on the SK model have been done to investigate aging
processes after a rapid quench from $T=\infty$ to the spin-glass phase. The
time range of simulations is taken care of so that the system does not surmount
free-energy barriers between the pure states which are considered to diverge in
the ther... | physics |
6,431 | Dynamics of particles and manifolds in a quenched random force field | cond-mat.dis-nn | We study the dynamics of a directed manifold of internal dimension D in a
d-dimensional random force field. We obtain an exact solution for $d \to
\infty$ and a Hartree approximation for finite d. They yield a Flory-like
roughness exponent $\zeta$ and a non trivial anomalous diffusion exponent $\nu$
continuously depend... | physics |
6,432 | From one cell to the whole froth: a dynamical map | cond-mat.dis-nn | We investigate two and three-dimensional shell-structured-inflatable froths,
which can be constructed by a recursion procedure adding successive layers of
cells around a germ cell. We prove that any froth can be reduced into a system
of concentric shells. There is only a restricted set of local configurations
for which... | physics |
6,433 | Finite Size Scaling Analysis of Exact Ground States for +/-J Spin Glass Models in Two Dimensions | cond-mat.dis-nn | With the help of EXACT ground states obtained by a polynomial algorithm we
compute the domain wall energy at zero-temperature for the bond-random and the
site-random Ising spin glass model in two dimensions. We find that in both
models the stability of the ferromagnetic AND the spin glass order ceases to
exist at a UNI... | physics |
6,434 | Fermion Mapping for Orthogonal and Symplectic Ensembles | cond-mat.dis-nn | The circular orthogonal and circular symplectic ensembles are mapped onto
free, non-hermitian fermion systems. As an illustration, the two-level form
factors are calculated. | physics |
6,435 | Long-time asymptotic of temporal-spatial coherence function for light propagation through time dependent disorder | cond-mat.dis-nn | Long-time asymptotic of field-field correlator for radiation propagated
through a medium composed of random point-like scatterers is studied using
Bete-Salpeter equation. It is shown that for plane source the fluctuation
intensity (zero spatial moment of the correlator) obeys a power-logarithmic
stretched exponential d... | physics |
6,436 | Statistical properties and shell analysis in random cellular structures | cond-mat.dis-nn | We investigate the statistical properties of two dimensional random cellular
systems (froths) in term of their shell structure. The froth is analyzed as a
system of concentric layers of cells around a given central cell. We derive
exact analytical relations for the topological properties of the sets of cells
belonging ... | physics |
6,437 | Quantum Monte Carlo simulations of a particle in a random potential | cond-mat.dis-nn | In this paper we carry out Quantum Monte Carlo simulations of a quantum
particle in a one-dimensional random potential (plus a fixed harmonic
potential) at a finite temperature. This is the simplest model of an interface
in a disordered medium and may also pertain to an electron in a dirty metal. We
compare with previo... | physics |
6,438 | Aging Relation for Ising Spin Glasses | cond-mat.dis-nn | We derive a rigorous dynamical relation on aging phenomena -- the aging
relation -- for Ising spin glasses using the method of gauge transformation.
The waiting-time dependence of the auto-correlation function in the
zero-field-cooling process is equivalent with that in the field-quenching
process. There is no aging on... | physics |
6,439 | Directed polymer in random media, in two dimensions: numerical study of the aging dynamics | cond-mat.dis-nn | Following a recent work by Yoshino, we study the aging dynamics of a directed
polymer in random media, in 1+1 dimensions. Through temperature quench, and
temperature cycling numerical experiments similar to the experiments on real
spin glasses, we show that the observed behaviour is comparable to the one of a
well know... | physics |
6,440 | The p-spin spherical spin glass model | cond-mat.dis-nn | This review presents various aspects of a mean-field spin glass model known
as the p-spin spherical spin glass model, which has raised a lot of interest in
the study of spin glasses, and also for its possible links with a mean-field
theory of structural glasses.
This preprint contains no new results and is therefore ... | physics |
6,441 | A Study of Activated Processes in Soft Sphere Glass | cond-mat.dis-nn | On the basis of long simulations of a binary mixture of soft spheres just
below the glass transition, we make an exploratory study of the activated
processes that contribute to the dynamics. We concentrate on statistical
measures of the size of the activated processes. | physics |
6,442 | History-Dependence and Ageing in a Periodic Long-Range Josephson Array | cond-mat.dis-nn | History-dependence and ageing are studied in the low-temperature glass phase
of a long-range periodic Josephson array. This model is characterized by two
parameters, the number of wires ($2N$) and the flux per unit strip ($\alpha$);
in the limit $N \to \infty$ and fixed $\alpha \ll 1$ the dynamics of the model
are desc... | physics |
6,443 | 1-loop contribution to the dynamical exponents in spin glasses | cond-mat.dis-nn | We evaluate the corrections to the mean field values of the $x$ and the $z$
exponents at the first order in the $\epsilon$-expansion, for $T=T_c $. We find
that both $x$ and $z$ are decreasing when the space dimension decreases. | physics |
6,444 | Power Tails of Electric Field Distribution Function in 2D Metal-Insulator Composites | cond-mat.dis-nn | The 2D "Swiss-cheese" model of conducting media with round insulator
inclusions is studied in the 2nd order of inclusion concentration and near the
percolation threshold. The electric field distribution function is found to
have power asymptotics for fields much exceeding the average field,
independently on the vicinit... | physics |
6,445 | Tempering simulations in the four dimensional +-J Ising spin glass in a magnetic field | cond-mat.dis-nn | We study the four dimensional (4D) $\pm J$ Ising spin glass in a magnetic
field by using the simulated tempering method recently introduced by Marinari
and Parisi. We compute numerically the first four moments of the order
parameter probability distribution $P(q)$. We find a finite cusp in the
spin-glass susceptibility... | physics |
6,446 | Data clustering using a model granular magnet | cond-mat.dis-nn | We present a new approach to clustering, based on the physical properties of
an inhomogeneous ferromagnet. No assumption is made regarding the underlying
distribution of the data. We assign a Potts spin to each data point and
introduce an interaction between neighboring points, whose strength is a
decreasing function o... | physics |
6,447 | Mean Green's function of the Anderson model at weak disorder with an infra-red cut-off | cond-mat.dis-nn | We develop a polymer expansion with large/small field conditions for the mean
resolvent of a weakly disordered system. Then we show that we can apply our
result to a two-dimensional model, for energies outside the unperturbed
spectrum or in the free spectrum provided the potential has an infra-red
cut-off. This leads t... | physics |
6,448 | Random copolymer: Gaussian variational approach | cond-mat.dis-nn | We study the phase transitions of a random copolymer chain with quenched
disorder. We apply a replica variational approach based on a Gaussian trial
Hamiltonian in terms of the correlation functions of monomer Fourier
coordinates. This allows us to study collapse, phase separation and freezing
transitions within the sa... | physics |
6,449 | Scale Invariance in Percolation Theory and Fractals | cond-mat.dis-nn | The properties of the similarity transformation in percolation theory in the
complex plane of the percolation probability are studied. It is shown that the
percolation problem on a two-dimensional square lattice reduces to the
Mandelbrot transformation, leading to a fractal behavior of the percolation
probability in th... | physics |
6,450 | Two interacting particles in a random potential: The random matrix model revisited | cond-mat.dis-nn | We reinvestigate the validity of mapping the problem of two onsite
interacting particles in a random potential onto an effective random matrix
model. To this end we first study numerically how the non-interacting basis is
coupled by the interaction. Our results indicate that the typical coupling
matrix element decrease... | physics |
6,451 | Density of States of an Electron in a Gaussian Random Potential for (4-epsilon)-dimensional Space | cond-mat.dis-nn | The density of states for the Schroedinger equation with a Gaussian random
potential is calculated in a space of dimension d=4-epsilon in the entire
energy range including the vicinity of a mobility edge. Leading terms in
1/epsilon are taken into account for N \sim 1 (N is an order of perturbation
theory) while all pow... | physics |
6,452 | Temperature evolution and bifurcations of metastable states in mean-field spin glasses, with connections with structural glasses | cond-mat.dis-nn | The correlations of the free-energy landscape of mean-field spin glasses at
different temperatures are investigated, concentrating on models with a first
order freezing transition. Using a ``potential function'' we follow the
metastable states of the model in temperature, and discuss the possibility of
level crossing (... | physics |
6,453 | Dynamical theory of quantum chaos or hidden random matrix ensemble? | cond-mat.dis-nn | In a recent Letter [Phys.Rev.Lett., 77,4536 (1996), chao-dyn/9609014] Altland
and Zirnbauer claim that they rigorously proved the complete analogy between a
(classically chaotic) dynamical system and disordered (random) solids. The
purpose of this Comment is to show that, in fact, their theory fails to take
into accoun... | physics |
6,454 | Phase Transitions in the Two-Dimensional XY Model with Random Phases: a Monte Carlo Study | cond-mat.dis-nn | We study the two-dimensional XY model with quenched random phases by Monte
Carlo simulation and finite-size scaling analysis. We determine the phase
diagram of the model and study its critical behavior as a function of disorder
and temperature. If the strength of the randomness is less than a critical
value, $\sigma_{c... | physics |
6,455 | Two Interacting Electrons in a Quasiperiodic Chain | cond-mat.dis-nn | We study numerically the effect of on-site Hubbard interaction U between two
electrons in the quasiperiodic Harper's equation. In the periodic chain limit
by mapping the problem to that of one electron in two dimensions with a
diagonal line of impurities of strength U we demonstrate a band of resonance
two particle pai... | physics |
6,456 | Replica Fourier Transforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices | cond-mat.dis-nn | The analysis of objects living on ultrametric trees, in particular the
block-diagonalization of 4-replica matrices $M^{\alpha \beta ; \gamma \delta}$,
is shown to be dramatically simplified through the introduction of properly
chosen operations on those objects. These are the Replica Fourier Transforms on
ultrametric t... | physics |
6,457 | Sparse random matrix configurations for two or three interacting electrons in a random potential | cond-mat.dis-nn | We investigate the random matrix configurations for two or three interacting
electrons in one-dimensional disordered systems. In a suitable non-interacting
localized electron basis we obtain a sparse random matrix with very long tails
which is different from a superimposed random band matrix usually thought to be
valid... | physics |
6,458 | Cubic Defects: Comparing the Eight-State-System with its Two-Level-Approximation | cond-mat.dis-nn | Substitutional defects in a cubic symmetry (such as a lithium defect in a KCl
host crystal) can be modeled appropriately by an eight-state-system. Usually
this tunneling degree of freedom is approximated by a two-level-system. We
investigate the observable differences between the two models in three
contexts. First we ... | physics |
6,459 | The electronic structure of amorphous silica: A numerical study | cond-mat.dis-nn | We present a computational study of the electronic properties of amorphous
SiO2. The ionic configurations used are the ones generated by an earlier
molecular dynamics simulations in which the system was cooled with different
cooling rates from the liquid state to a glass, thus giving access to
glass-like configurations... | physics |
6,460 | Spreading of Damage in the SK Spherical Spin Glass | cond-mat.dis-nn | By considering the Langevin dynamics of the SK spin glass with a spherical
constraint we calculate the asymptotic distance between two real replicas that
evolve with the same thermal noise from different initial conditions. Despite
the simplicity of the model its dynamics is known to be non trivial and
presents aging p... | physics |
6,461 | A hierarchical model for aging | cond-mat.dis-nn | We present a one dimensional model for diffusion on a hierarchical tree
structure. It is shown that this model exhibits aging phenomena although no
disorder is present. The origin of aging in this model is therefore the
hierarchical structure of phase space. | physics |
6,462 | Molecular Dynamics Computer Simulation of the Dynamics of Supercooled Silica | cond-mat.dis-nn | We present the results of a large scale computer simulation of supercooled
silica. We find that at high temperatures the diffusion constants show a
non-Arrhenius temperature dependence whereas at low temperature this dependence
is also compatible with an Arrhenius law. We demonstrate that at low
temperatures the interm... | physics |
6,463 | Ground state structure of diluted antiferromagnets and random field systems | cond-mat.dis-nn | A method is presented for the calculation of all exact ground states of
diluted antiferromagnets and random field systems in an arbitrary range of
fields. It works by calculating all jump-fields B,\Delta where the system
changes it's ground state. For each field value all degenerated ground states
are represented by a ... | physics |
6,464 | Study of the ultrametric structure of Finite Dimensional Spin Glasses throught a constrained Monte Carlo dynamics | cond-mat.dis-nn | We report a very detailed relation about the study, by a constrained Monte
Carlo dynamic, of a 4D EA spin glass model (J=+/- 1). In particular we
concentrate our attention on the behaviour of the system under different bounds
imposed in order to optimize the dynamic and try to understand the low energy
states structure... | physics |
6,465 | Classical Advection of Guiding Centers in a Random Magnetic Field | cond-mat.dis-nn | We investigate theoretically and experimentally classical advective transport
in a 2D electron gas in a random magnetic field. For uniform external
perpendicular magnetic fields large compared to the random field we observe a
strong enhancement of conductance compared to the ordinary Drude value. This
can be understood... | physics |
6,466 | Quantum Vibrational Impurity Embedded in a One-dimensional Chain | cond-mat.dis-nn | We perform a fully quantum mechanical numerical calculation for the problem
of a single electron (or excitation) propagating in a N-site one-dimensional
chain in the presence of a single Holstein impurity. We compute the long-time
averaged probability for finding the electron on the impurity site as a
function of the n... | physics |
6,467 | Parallel dynamics of fully connected Q-Ising neural networks | cond-mat.dis-nn | Using a probabilistic approach we study the parallel dynamics of fully
connected Q-Ising neural networks for arbitrary Q. A Lyapunov function is shown
to exist at zero temperature. A recursive scheme is set up to determine the
time evolution of the order parameters through the evolution of the
distribution of the local... | physics |
6,468 | The Blume-Emery-Griffiths Spin Glass Model | cond-mat.dis-nn | We study the equilibrium properties of the Blume-Emery-Griffiths model with
bilinear quenched disorder in the case of attractive as well as repulsive
biquadratic interactions. The global phase diagram of the system is calculated
in the context of the replica symmetric mean field approximation. | physics |
6,469 | Quantum Critical Dynamics of the Random Transverse Field Ising Spin Chain | cond-mat.dis-nn | Dynamical correlations of the spin and the energy density are investigated in
the critical region of the random transverse-field Ising chain by numerically
exact calculations in large finite systems (L<=128). The spin-spin
autocorrelation function is found to decay proportional to (log t)^{-2x_m} and
(log t)^{-2x_m^s} ... | physics |
6,470 | Evidence for existence of many pure ground states in 3d $\pm J$ Spin Glasses | cond-mat.dis-nn | Ground states of 3d EA Ising spin glasses are calculated for sizes up to
$14^3$ using a combination of genetic algorithms and cluster-exact
approximation . The distribution $P(|q|)$ of overlaps is calculated. For
increasing size the width of $P(|q|)$ converges to a nonzero value, indicating
that many pure ground states... | physics |
6,471 | Nonlinear acoustic and microwave absorption in glasses | cond-mat.dis-nn | A theory of weakly-nonlinear low-temperature relaxational absorption of
acoustic and electromagnetic waves in dielectric and metallic glasses is
developed. Basing upon the model of two-level tunneling systems we show that
the nonlinear contribution to the absorption can be anomalously large. This is
the case at low eno... | physics |
6,472 | Dynamics of an electron in finite and infinite one dimensional systems in presence of electric field | cond-mat.dis-nn | We study,numerically, the dynamical behavior of an electron in a two site
nonlinear system driven by dc and ac electric field separately. We also study,
numerically, the effect of electric field on single static impurity and
antidimeric dynamical impurity in an infinite 1D chain to find the strength of
the impurities. ... | physics |
6,473 | Mean-field theory for a spin-glass model of neural networks: TAP free energy and paramagnetic to spin-glass transition | cond-mat.dis-nn | An approach is proposed to the Hopfield model where the mean-field treatment
is made for a given set of stored patterns (sample) and then the statistical
average over samples is taken. This corresponds to the approach made by
Thouless, Anderson and Palmer (TAP) to the infinite-range model of spin
glasses. Taking into a... | physics |
6,474 | High-Temperature Dynamics of Spin Glasses | cond-mat.dis-nn | We develop a systematic expansion method of physical quantities for the SK
model and the finite-dimensional $\pm J$ model of spin glasses in
non-equilibrium states. The dynamical probability distribution function is
derived from the master equation using a high temperature expansion. We
calculate the expectation values... | physics |
6,475 | Ultrametric Matrices and Representation Theory | cond-mat.dis-nn | The consequences of replica-symmetry breaking on the structure of ultrametric
matrices appearing in the theory of disordered systems is investigated with the
help of representation theory, and the results are compared with those obtained
by Temesvari, De Dominicis and Kondor. | physics |
6,476 | 2d frustrated Ising model with four phases | cond-mat.dis-nn | In this paper we consider a 2d random Ising system on a square lattice with
nearest neighbour interactions. The disorder is short range correlated and
asymmetry between the vertical and the horizontal direction is admitted. More
precisely, the vertical bonds are supposed to be non random while the
horizontal bonds alte... | physics |
6,477 | The role of power law nonlinearity in the discrete nonlinear Schrödinger equation on the formation of stationary localized states in the Cayley tree | cond-mat.dis-nn | We study the formation of stationary localized states using the discrete
nonlinear Schr\"{o}dinger equation in a Cayley tree with connectivity $K$. Two
cases, namely, a dimeric power law nonlinear impurity and a fully nonlinear
system are considered. We introduce a transformation which reduces the Cayley
tree into an o... | physics |
6,478 | Non-exponential relaxation in diluted antiferromagnets | cond-mat.dis-nn | Diluted Ising antiferromagnets in a homogenous magnetic field have a
disordered phase for sufficiently large values of the field and for low
temperatures. Here, the system is in a domain state with a broad
size-distribution of fractal domains. We study the relaxation dynamics of this
domain state after removing the ext... | physics |
6,479 | Exact solution of a 2d random Ising model | cond-mat.dis-nn | The model considered is a d=2 layered random Ising system on a square lattice
with nearest neighbours interaction. It is assumed that all the vertical
couplings are equal and take the positive value J while the horizontal
couplings are quenched random variables which are equal in the same row but can
take the two possi... | physics |
6,480 | A solvable model of a random spin-1/2 XY chain | cond-mat.dis-nn | The paper presents exact calculations of thermodynamic quantities for the
spin-1/2 isotropic XY chain with random lorentzian intersite interaction and
transverse field that depends linearly on the surrounding intersite
interactions. | physics |
6,481 | Generalization ability of a perceptron with non-monotonic transfer function | cond-mat.dis-nn | We investigate the generalization ability of a perceptron with non-monotonic
transfer function of a reversed-wedge type in on-line mode. This network is
identical to a parity machine, a multilayer network. We consider several
learning algorithms. By the perceptron algorithm the generalization error is
shown to decrease... | physics |
6,482 | Dynamical properties of the hypercell spin glass model | cond-mat.dis-nn | The spreading of damage technique is used to study the sensibility to initial
conditions in a heath bath Monte Carlo simulation of the spin glass hypercubic
cell model. Since the hypercubic cell in dimension 2D and the hypercubic
lattice in dimension D resemble each other closely at finite dimensions and
both converge ... | physics |
6,483 | Dimensional Crossover of Weak Localization in a Magnetic Field | cond-mat.dis-nn | We study the dimensional crossover of weak localization in strongly
anisotropic systems. This crossover from three-dimensional behavior to an
effective lower dimensional system is triggered by increasing temperature if
the phase coherence length gets shorter than the lattice spacing $a$. A similar
effect occurs in a ma... | physics |
6,484 | Statistical Mechanical Analysis of the Dynamics of Learning in Perceptrons | cond-mat.dis-nn | We describe the application of tools from statistical mechanics to analyse
the dynamics of various classes of supervised learning rules in perceptrons.
The character of this paper is mostly that of a cross between a biased
non-encyclopedic review and lecture notes: we try to present a coherent and
self-contained pictur... | physics |
6,485 | Bounds on learning in polynomial time | cond-mat.dis-nn | The performance of large neural networks can be judged not only by their
storage capacity but also by the time required for learning. A polynomial
learning algorithm with learning time $\sim N^2$ in a network with $N$ units
might be practical whereas a learning time $\sim e^N$ would allow rather small
networks only. Th... | physics |
6,486 | Scaling of the Random-Field Ising Model at Zero Temperature | cond-mat.dis-nn | The exact determination of ground states of small systems is used in a
scaling study of the random-field Ising model. While three variants of the
model are found to be in the same universality class in 3 dimensions, the
Gaussian and bimodal models behave distinctly in 4 dimensions with the latter
apparently having a di... | physics |
6,487 | Functional Optimisation of Online Algorithms in Multilayer Neural Networks | cond-mat.dis-nn | We study the online dynamics of learning in fully connected soft committee
machines in the student-teacher scenario. The locally optimal modulation
function, which determines the learning algorithm, is obtained from a
variational argument in such a manner as to maximise the average generalisation
error decay per exampl... | physics |
6,488 | An investigation of the hidden structure of states in a mean field spin glass model | cond-mat.dis-nn | We study the geometrical structure of the states in the low temperature phase
of a mean field model for generalized spin glasses, the p-spin spherical model.
This structure cannot be revealed by the standard methods, mainly due to the
presence of an exponentially high number of states, each one having a vanishing
weigh... | physics |
6,489 | Dynamical heterogeneities in a supercooled Lennard-Jones liquid | cond-mat.dis-nn | We present the results of a large scale molecular dynamics computer
simulation study in which we investigate whether a supercooled Lennard-Jones
liquid exhibits dynamical heterogeneities. We evaluate the non-Gaussian
parameter for the self part of the van Hove correlation function and use it to
identify ``mobile'' part... | physics |
6,490 | Metastates in the Hopfield model in the replica symmetric regime | cond-mat.dis-nn | We study the finite dimensional marginals of the Gibbs measure in the
Hopfield model at low temperature when the number of patterns, $M$, is
proportional to the volume with a sufficiently small proportionality constant
$\a>0$. It is shown that even when a single pattern is selected (by a magnetic
field or by conditioni... | physics |
6,491 | Low-frequency Raman scattering in model disordered solids: percolators above threshold | cond-mat.dis-nn | The Raman coupling coefficients of site- and bond-percolators at
concentration higher than percolation threshold are computed for two scattering
mechanisms: Bond Polarizability (BPOL) and Dipole-Induced-Dipole (DID). The
results show that DID does not follow a scaling law at low frequency, while in
the case of BPOL the... | physics |
6,492 | Quantum phase transition in spin glasses with multi-spin interactions | cond-mat.dis-nn | We examine the phase diagram of the $p$-interaction spin glass model in a
transverse field. We consider a spherical version of the model and compare with
results obtained in the Ising case. The analysis of the spherical model, with
and without quantization, reveals a phase diagram very similar to that obtained
in the I... | physics |
6,493 | The two-dimensional Anderson model of localization with random hopping | cond-mat.dis-nn | We examine the localization properties of the 2D Anderson Hamiltonian with
off-diagonal disorder. Investigating the behavior of the participation numbers
of eigenstates as well as studying their multifractal properties, we find
states in the center of the band which show critical behavior up to the system
size $N= 200 ... | physics |
6,494 | String-like Clusters and Cooperative Motion in a Model Glass-Forming Liquid | cond-mat.dis-nn | A large-scale molecular dynamics simulation is performed on a glass-forming
Lennard-Jones mixture to determine the nature of dynamical heterogeneities
which arise in this model fragile liquid. We observe that the most mobile
particles exhibit a cooperative motion in the form of string-like paths
(``strings'') whose mea... | physics |
6,495 | Study of transmission and reflection from a disordered lasing medium | cond-mat.dis-nn | A numerical study of the statistics of transmission ($t$) and reflection
($r$) of quasi-particles from a one-dimensional disordered lasing or amplifying
medium is presented. The amplification is introduced via a uniform imaginary
part in the site energies in the disordered segment of the single-band tight
binding model... | physics |
6,496 | Energy functional and fixed points of a neural network | cond-mat.dis-nn | A dynamic system, which is used in the neural network theory, Ising spin
glasses and factor analysis, has been investigated. The properties of the
connection matrix, which guarantee the coincidence of the set of the fixed
points of the dynamic system with the set of the local minima of the energy
functional, have been ... | physics |
6,497 | Stationary localized states due to quadratic nonlinearity in one dimensional systems | cond-mat.dis-nn | We investigate the effect of a nondegenerate quadratic nonlinear dimeric
impurity on the formation of stationary localized states in one dimensional
systems. We also consider the formation of stationary localized states in a
fully nonlinear system where alternative sites have same nonlinear strengths.
Appropriate ansat... | physics |
6,498 | On the distribution of the Wigner time delay in one-dimensional disordered systems | cond-mat.dis-nn | We consider the scattering by a one-dimensional random potential and derive
the probability distribution of the corresponding Wigner time delay. It is
shown that the limiting distribution is the same for two different models and
coincides with the one predicted by random matrix theory. It is also shown that
the corresp... | physics |
6,499 | Universality Classes for Extreme Value Statistics | cond-mat.dis-nn | The low temperature physics of disordered systems is governed by the
statistics of extremely low energy states. It is thus rather important to
discuss the possible universality classes for extreme value statistics. We
compare the usual probabilistic classification to the results of the replica
approach. We show in deta... | physics |
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