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

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

Translation invariant Gibbs states for the Ising model

Auteur(s):

Code(s) de Classification MSC:

Résumé: We prove that all the translation invariant Gibbs states of the Ising model are a linear combination of the pure phases $\mu^+_\gb,\mu^-_\gb$ for any $\gb \not = \gb_c$. This implies that the average magnetization is continuous for $\gb >\gb_c$. Furthermore, combined with previous results on the slab percolation threshold this shows the validity of Pisztora's coarse graining up to the critical temperature.

Mots Clés: Ising model ; Gibbs measures

Date: 2004-09-27

Prépublication numéro: PMA-937