Ensemble inequivalence in random graphs

TL;DR

This paper analytically investigates ensemble inequivalence in a Potts spin system on random graphs, revealing non-concave entropy and negative specific heat regions through the Large Deviation Cavity Method and simulations.

Contribution

It provides the first complete analytical solution of Potts spins on random regular graphs in both ensembles, highlighting ensemble inequivalence and non-concave entropy.

Findings

Presence of negative specific heat region

Demonstration of ensemble inequivalence

Confirmation via numerical simulations

Abstract

We present a complete analytical solution of a system of Potts spins on a random k-regular graph in both the canonical and microcanonical ensembles, using the Large Deviation Cavity Method (LDCM). The solution is shown to be composed of three different branches, resulting in an non-concave entropy function.The analytical solution is confirmed with numerical Metropolis and Creutz simulations and our results clearly demonstrate the presence of a region with negative specific heat and, consequently, ensemble inequivalence between the canonical and microcanonical ensembles.