Equilibrium States of the Ising Model in the Two-Phase Region

Abstract

We prove that at low enough temperature all translationally invariant equilibrium states for the Ising ferromagnet are a superposition of only two extremal states, i.e., the positively and negatively magnetized pure phases. In particular this proves, at low temperature and in two dimensions, the identity of the spontaneous magnetization and the Onsager's value $M_0={[1-{\left(sh\beta \right)}^{-4\mathrm{}}]}^{\frac{1}{8}}$.