# Translation invariant Gibbs states for the Ising model

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1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Abstract : 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 $\gb ot = \gb c$. 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.

Keywords : Ising model Gibbs measures

Autor: Thierry Bodineau -

Fuente: https://hal.archives-ouvertes.fr/

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