Translation invariant Gibbs states for the Ising model

Thierry Bodineau (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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

Domaines: Probabilités [math.PR]

Thierry Bodineau. Translation invariant Gibbs states for the Ising model. 2004. ⟨hal-00003038⟩