Uniqueness of Gibbs State for Nonideal Gas in ℝ^d: The Case of Pair Potentials

Abstract

We consider a classical gas of particles in ℝ^d interacting via a pair potential. We prove that in a given region of the (β, μ) plane, where β is the inverse temperature, and μ is the chemical potential, either the Gibbs state is unique or it does not exist. Our method uses a version of the well-known Dobrushin uniqueness theorem adapted for lattice systems with a noncompact spin space and proved by Dobrushin and Pechersky. The advantage of this version is that using it one needs to check Dobrushin's contraction condition not for all boundary configurations, but only for those that have spin values in some compact subset of the spin space.