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

摘要: 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., positively and negatively magnetized pure phases. In particular this proves, in dimensions, identity spontaneous magnetization Onsager's value ${M}_{0}={[1\ensuremath{-}{(sh\ensuremath{\beta})}^{\ensuremath{-}4}]}^{\frac{1}{8}}$.