Sharp asymptotics for metastability in the random field Curie-Weiss model

TL;DR

This paper provides precise estimates on metastable behavior in the random field Curie-Weiss model, extending previous results to cases with continuous random fields using potential theory.

Contribution

It introduces the first sharp estimates for metastability in the model with continuous random fields, overcoming limitations of previous finite-value assumptions.

Findings

Sharp estimates on capacities and exit times derived

Extension of potential theoretic methods to continuous distributions

First results incorporating entropy effects in metastability analysis

Abstract

In this paper we study the metastable behavior of one of the simplest disordered spin system, the random field Curie-Weiss model. We will show how the potential theoretic approach can be used to prove sharp estimates on capacities and metastable exit times also in the case when the distribution of the random field is continuous. Previous work was restricted to the case when the random field takes only finitely many values, which allowed the reduction to a finite dimensional problem using lumping techniques. Here we produce the first genuine sharp estimates in a context where entropy is important.