Translation invariant Gibbs states for the Ising model
Abstract
Description
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.
14 pages, 3 figures
14 pages, 3 figures