Extension of Pirogov-Sinai theory of phase transitions to infinite range interactions. I: Cluster expansion (Q1114236)

This paper is the first part of an extension of the Pirogov-Sinai theory of phase transitions at low temperatures, applicable to lattice systems with finite range interactions, to infinite range interactions. Transforming the systems to a version of an interacting contour model, we develop a cluster expansion. Making appropriate assumptions about the interactions, we prove that for sufficiently low temperatures the expansion converges and the cluster property holds.