2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72375We 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 figuresProbability82B20; 82B26text