Extension of Pirogov-Sinai theory of phase transitions to infinite range interactions. II. Phase diagram

Abstract

This paper is the second part of our attempt of an extension of the Pirogov-Sinai theory of phase transitions at low temperatures, applicable to the lattice spin systems with finite range interactions, to the systems with infinite range interactions. Employing the cluster expansion method developed in Part I and modifying the notion of the truncated contour model introduced by Zahradnik, we extend the Pirogov-Sinai result on the structure of phase diagrams to our situations. As an application, we apply our result to Potts models with infinite range interactions.