136 research outputs found
Temporal Correlations and Persistence in the Kinetic Ising Model: the Role of Temperature
We study the statistical properties of the sum , that is the difference of time spent positive or negative by the
spin , located at a given site of a -dimensional Ising model
evolving under Glauber dynamics from a random initial configuration. We
investigate the distribution of and the first-passage statistics
(persistence) of this quantity. We discuss successively the three regimes of
high temperature (), criticality (), and low temperature
(). We discuss in particular the question of the temperature
dependence of the persistence exponent , as well as that of the
spectrum of exponents , in the low temperature phase. The
probability that the temporal mean was always larger than the
equilibrium magnetization is found to decay as . This
yields a numerical determination of the persistence exponent in the
whole low temperature phase, in two dimensions, and above the roughening
transition, in the low-temperature phase of the three-dimensional Ising model.Comment: 21 pages, 11 PostScript figures included (1 color figure
The Kovacs effect in model glasses
We discuss the `memory effect' discovered in the 60's by Kovacs in
temperature shift experiments on glassy polymers, where the volume (or energy)
displays a non monotonous time behaviour. This effect is generic and is
observed on a variety of different glassy systems (including granular
materials). The aim of this paper is to discuss whether some microscopic
information can be extracted from a quantitative analysis of the `Kovacs hump'.
We study analytically two families of theoretical models: domain growth and
traps, for which detailed predictions of the shape of the hump can be obtained.
Qualitatively, the Kovacs effect reflects the heterogeneity of the system: its
description requires to deal not only with averages but with a full probability
distribution (of domain sizes or of relaxation times). We end by some
suggestions for a quantitative analysis of experimental results.Comment: 17 pages, 6 figures; revised versio
Coarsening and persistence in a class of stochastic processes interpolating between the Ising and voter models
We study the dynamics of a class of two dimensional stochastic processes,
depending on two parameters, which may be interpreted as two different
temperatures, respectively associated to interfacial and to bulk noise. Special
lines in the plane of parameters correspond to the Ising model, voter model and
majority vote model. The dynamics of this class of models may be described
formally in terms of reaction diffusion processes for a set of coalescing,
annihilating, and branching random walkers. We use the freedom allowed by the
space of parameters to measure, by numerical simulations, the persistence
probability of a generic model in the low temperature phase, where the system
coarsens. This probability is found to decay at large times as a power law with
a seemingly constant exponent . We also discuss the
connection between persistence and the nature of the interfaces between
domains.Comment: Late
A simple stochastic model for the dynamics of condensation
We consider the dynamics of a model introduced recently by Bialas, Burda and
Johnston. At equilibrium the model exhibits a transition between a fluid and a
condensed phase. For long evolution times the dynamics of condensation
possesses a scaling regime that we study by analytical and numerical means. We
determine the scaling form of the occupation number probabilities. The
behaviour of the two-time correlations of the energy demonstrates that aging
takes place in the condensed phase, while it does not in the fluid phase.Comment: 8 pages, plain tex, 2 figure
Replica analysis of a preferential urn model
We analyse a preferential urn model with randomness using the replica method.
The preferential urn model is a stochastic model based on the concept "the rich
get richer." The replica analysis clarifies that the preferential urn model
with randomness shows a fat-tailed occupation distribution. The analytical
treatments and results would be useful for various research fields such as
complex networks, stochastic models, and econophysics.Comment: 6 pages, 2 figure
Structure of the stationary state of the asymmetric target process
We introduce a novel migration process, the target process. This process is
dual to the zero-range process (ZRP) in the sense that, while for the ZRP the
rate of transfer of a particle only depends on the occupation of the departure
site, it only depends on the occupation of the arrival site for the target
process. More precisely, duality associates to a given ZRP a unique target
process, and vice-versa. If the dynamics is symmetric, i.e., in the absence of
a bias, both processes have the same stationary-state product measure. In this
work we focus our interest on the situation where the latter measure exhibits a
continuous condensation transition at some finite critical density ,
irrespective of the dimensionality. The novelty comes from the case of
asymmetric dynamics, where the target process has a nontrivial fluctuating
stationary state, whose characteristics depend on the dimensionality. In one
dimension, the system remains homogeneous at any finite density. An alternating
scenario however prevails in the high-density regime: typical configurations
consist of long alternating sequences of highly occupied and less occupied
sites. The local density of the latter is equal to and their
occupation distribution is critical. In dimension two and above, the asymmetric
target process exhibits a phase transition at a threshold density much
larger than . The system is homogeneous at any density below ,
whereas for higher densities it exhibits an extended condensate elongated along
the direction of the mean current, on top of a critical background with density
.Comment: 30 pages, 16 figure
Dynamics of the condensate in zero-range processes
For stochastic processes leading to condensation, the condensate, once it is
formed, performs an ergodic stationary-state motion over the system. We analyse
this motion, and especially its characteristic time, for zero-range processes.
The characteristic time is found to grow with the system size much faster than
the diffusive timescale, but not exponentially fast. This holds both in the
mean-field geometry and on finite-dimensional lattices. In the generic
situation where the critical mass distribution follows a power law, the
characteristic time grows as a power of the system size.Comment: 27 pages, 7 figures. Minor changes and updates performe
Models of competitive learning: complex dynamics, intermittent conversions and oscillatory coarsening
We present two models of competitive learning, which are respectively
interfacial and cooperative learning. This learning is outcome-related, so that
spatially and temporally local environments influence the conversion of a given
site between one of two different types. We focus here on the behavior of the
models at coexistence, which yields new critical behavior and the existence of
a phase involving a novel type of coarsening which is oscillatory in nature.Comment: 23 pages, 11 figures. To appear in Phys. Rev.
Search for Fermion Actions on Hyperdiamond Lattices
Fermions moving in a two-dimensional honeycomb lattice (graphene) have, at
low energies, chiral symmetry. Generalizing this construction to four
dimensions potentially provides fermions with chiral symmetry and only the
minimal fermion doubling demanded by the Nielsen-Ninomiya no-go theorem. The
practical usefulness of such fermions hinges on whether the action has a
necessary set of discrete symmetries of the lattice. If this is the case, one
avoids the generation of dimension three and four operators which require fine
tuning. We construct hyperdiamond lattice actions with enough symmetries to
exclude fine tuning; however, they produce multiple doublings. The limit where
the actions exhibit minimal doubling does not possess the requisite symmetry.Comment: 4 pages, 1 figur
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