Coexistence of ordered and disordered phases in Potts models in the continuum

TL;DR

This paper demonstrates the coexistence of ordered and disordered phases in a continuum Potts model with multiple spin states, showing phase transitions via multiple Gibbs measures at certain parameters.

Contribution

It proves the existence of phase transitions in a continuum Potts model with multiple spins using Kac potentials, extending previous discrete models.

Findings

Existence of multiple DLR measures indicating phase coexistence

Phase transition occurs at specific temperature and chemical potential

Presence of ordered and disordered phases in the continuum setting

Abstract

This is the second of two papers on a continuum version of the Potts model, where particles are points in $\mathbb R^d$, $d\ge 2$, with a spin which may take $S\ge 3$ possible values. Particles with different spins repel each other via a Kac pair potential of range $\ga^{-1}$, $\ga>0$. 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.