Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Stability of interfaces and stochastic dynamics in the regime of partial wetting


Code(s) de Classification MSC:

Résumé: The goal of this paper is twofold. First, assuming strict convexity of the surface tension, we derive a stability property with respect to the Hausdorff distance of a coarse grained representation of the interface between the two pure phases of the Ising model. This improves the $\bbL^1$ description of phase segregation. Using this result and an additional assumption on mixing properties of the underlying FK measures, we are then able to extend to higher dimensions previous results by Martinelli \cite{Ma} on the spectral gap of the two-dimensional Glauber dynamics. Our assumptions can be easily verified for low enough temperatures and, presumably, hold true in the whole of the phase coexistence region.

Mots Clés: Ising ; Phase transition ; Interfaces ; Glauber dynamics ; Spectral gap

Date: 2003-11-26

Prépublication numéro: PMA-868