15,934 research outputs found

### Surface Tension in Kac Glass Models

In this paper we study a distance-dependent surface tension, defined as the
free-energy cost to put metastable states at a given distance. This will be
done in the framework of a disordered microscopic model with Kac interactions
that can be solved in the mean-field limit.Comment: 13 pages, 6 figure

### Spin glass models with Kac interactions

In this paper I will review my work on disordered systems -spin glass model
with two body and $p>2$ body interactions- with long but finite interaction
range $R$. I will describe the relation of these model with Mean Field Theory
in the Kac limit and some attempts to go beyond mean field.Comment: Proceedings of the Stat-phys23 conferenc

### A note on the Guerra and Talagrand theorems for Mean Field Spin Glasses: the simple case of spherical models

The aim of this paper is to discuss the main ideas of the Talagrand proof of
the Parisi Ansatz for the free-energy of Mean Field Spin Glasses with a
physicist's approach. We consider the case of the spherical $p$-spin model,
which has the following advantages: 1) the Parisi Ansatz takes the simple ``one
step replica symmetry breaking form'', 2) the replica free-energy as a function
of the order parameters is simple enough to allow for numerical maximization
with arbitrary precision. We present the essential ideas of the proof, we
stress its connections with the theory of effective potentials for glassy
systems, and we reduce the technically more difficult part of the Talagrand's
analysis to an explicit evaluation of the solution of a variational problem.Comment: 20 pages, 5 figures. Added references and minor language correction

### Metastable States, Relaxation Times and Free-energy Barriers in Finite Dimensional Glassy Systems

In this note we discuss metastability in a long-but-finite range disordered
model for the glass transition. We show that relaxation is dominated by
configuration belonging to metastable states and associate an in principle
computable free-energy barrier to the equilibrium relaxation time. Adam-Gibbs
like relaxation times appear naturally in this approach.Comment: 4 pages, 2 figures. Typos correcte

### Analytic determination of dynamical and mosaic length scales in a Kac glass model

We consider a disordered spin model with multi-spin interactions undergoing a
glass transition. We introduce a dynamic and a static length scales and compute
them in the Kac limit (long--but--finite range interactions). They diverge at
the dynamic and static phase transition with exponents (respectively) -1/4 and
-1. The two length scales are approximately equal well above the mode coupling
transition. Their discrepancy increases rapidly as this transition is
approached. We argue that this signals a crossover from mode coupling to
activated dynamics.Comment: 4 pages, 4 eps figures. New version conform to the published on

### 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

### Series Expansion of the Off-Equilibrium Mode Coupling Equations

We show that computing the coefficients of the Taylor expansion of the
solution of the off-equilibrium dynamical equations characterizing models with
quenched disorder is a very effective way to understand the long time
asymptotic behavior. We study the $p=3$ spherical spin glass model, and we
compute the asymptotic energy (in the critical region and down to $T=0$) and
the coefficients of the time decay of the energy.Comment: 9 pages, LaTeX, 3 uuencoded figure

### On chaos in mean field spin glasses

We study the correlations between two equilibrium states of SK spin glasses
at different temperatures or magnetic fields. The question, presiously
investigated by Kondor and Kondor and V\'egs\"o, is approached here
constraining two copies of the same system at different external parameters to
have a fixed overlap. We find that imposing an overlap different from the
minimal one implies an extensive cost in free energy. This confirms by a
different method the Kondor's finding that equilibrium states corresponding to
different values of the external parameters are completely uncorrelated. We
also consider the Generalized Random Energy Model of Derrida as an example of
system with strong correlations among states at different temperatures.Comment: 19 pages, Late

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