Coexistence of Ordered and Disordered Phases in Potts Models in the Continuum

Abstract

This is the second of two papers on a continuum version of the Potts model, where particles are points in ℝ d , d≥2, with a spin which may take S≥3 possible values. Particles with different spins repel each other via a Kac pair potential of range γ −1, γ>0. In this paper we prove phase transition, namely we prove that if the scaling parameter of the Kac potential is suitably small, given any temperature there is a value of the chemical potential such that at the given temperature and chemical potential there exist S+1 mutually distinct DLR measures.