Translation invariant Gibbs states for the Ising model

Details Translation invariant Gibbs states for the Ising model Translation invariant Gibbs states for the Ising model

2004-09-06

arxiv.org/abs/math/0409079v1

Mathematics

Probability

14 pages, 3 figures

Scientific paper

We prove that all the translation invariant Gibbs states of the Ising model are a linear combination of the pure phases $\mu^+,\mu^-$ in the phase transition regime. This implies that the average magnetization is continuous in the phase transition regime ($\beta > \beta_c$). 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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