Translation invariant Gibbs states for the Ising model

T. Bodineau

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Translation invariant Gibbs states for the Ising model

T. Bodineau

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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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T. Bodineau. 2004-09-06. Translation invariant Gibbs states for the Ising model. https://arxiv.org/abs/math/0409079

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