Absence of Phase Transitions in Hard-Core One-Dimensional Systems with Long-Range Interactions

Abstract

We prove the impossibility of phase transitions for a class of infinite‐range potentials extending recent analogous results. We prove also a cluster property for the equilibrium state γ̄ and apply some collateral results to describe, in the case of finite‐range interactions, the state γ̄ in terms of a family of density distributions, and to verify a general variational property of γ̄ .