Ensemble equivalence in spin systems with short-range interactions

TL;DR

This paper investigates ensemble equivalence in short-range interacting spin systems at first-order phase transitions, revealing apparent inequivalence in the spherical model and proposing a phase separation resolution, supported by simulations of the XY model.

Contribution

It provides an exact solution for the spherical model showing ensemble inequivalence and introduces an unconventional saddle point to resolve the paradox, also comparing with XY model simulations.

Findings

Microcanonical entropy is non-concave at the transition point.

Negative specific heat indicates ensemble inequivalence.

Phase separation resolves the apparent paradox.

Abstract

We study the problem of ensemble equivalence in spin systems with short-range interactions under the existence of a first-order phase transition. The spherical model with nonlinear nearest-neighbour interactions is solved exactly both for canonical and microcanonical ensembles. The result reveals apparent ensemble inequivalence at the first-order transition point in the sense that the microcanonical entropy is non-concave as a function of the energy and consequently the specific heat is negative. In order to resolve the paradox, we show that an unconventional saddle point should be chosen in the microcanonical calculation that represents a phase separation. The XY model with non-linear interactions is also studied by microcanonical Monte Carlo simulations in two dimensions to see how this model behaves in comparison with the spherical model.