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 Electronic Journal of Probability > Vol. 14 (2009) > Paper 53 open journal systems 


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

Alessandra Bianchi, Weierstrass Institute for Applied Analysis and Stochastics (WIAS)
Anton Bovier, Institut für Angewandte Mathematik Rheinische Friedrich-Wilhelms-Universität
Dmitry Ioffe, William Davidson Faculty of Industrial Engineering and Management Technion


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.


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Pages: 1541-1603

Published on: July 9, 2009
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Electronic Journal of Probability. ISSN: 1083-6489