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

• 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
• 82B26 Phase transitions (general)

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