Translation invariant Gibbs states for the Ising model

2004/09/06 by T. Bodineau, Bodineau, T.
Mathematics · Physics and Astronomy · #82B20 #82B26 #FOS: Mathematics #Probability (math.PR) #Statistical Mechanics and Entropy #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:82B20 #msc:82B26

paper · pdf · doi:10.48550/arxiv.math/0409079

14 pages, 3 figures

arxiv created 2004/09/06 · openalex publication_date 2004/09/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that all the translation invariant Gibbs states of the Ising model are a linear combination of the pure phases μ⁺,μ^- in the phase transition regime. This implies that the average magnetization is continuous in the phase transition regime (β> β_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.

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