On the Uniqueness of Gibbs States in the Pirogov–sinai Theory

Abstract

We consider models of classical statistical mechanics satisfying natural stability conditions: a finite spin space, translation-periodic finite potential of finite range, a finite number of ground states meeting Peierls or Gertzik-Pirogov-Sinai condition. The Pirogov-Sinai theory describes the phase diagrams of these models at low temperature regimes. By using the method of doubling and mixing of partition functions we give an alternative elementary proof of the uniqueness of limiting Gibbs states at low temperatures in ground state uniqueness region.