Ensemble inequivalence : Landau theory and the ABC model

TL;DR

This paper investigates how ensemble inequivalence in systems with long-range interactions relates to the symmetry of the order parameter, using Landau theory and the ABC model as a case study.

Contribution

It establishes a connection between the order of phase transitions and symmetry properties of the order parameter in long-range interacting systems.

Findings

Ensemble inequivalence can occur at continuous transitions.

Symmetry properties of the order parameter influence the transition order.

Landau expansion analysis confirms the theoretical predictions.

Abstract

It is well known that systems with long-range interactions may exhibit different phase diagrams when studied within two different ensembles. In many of the previously studied examples of ensemble inequivalence, the phase diagrams differ only when the transition in one of the ensembles is first order. By contrast, in a recent study of a generalized ABC model, the canonical and grand-canonical ensembles of the model were shown to differ even when they both exhibit a continuous transition. Here we show that the order of the transition where ensemble inequivalence may occur is related to the symmetry properties of the order parameter associated with the transition. This is done by analyzing the Landau expansion of a generic model with long-range interactions. The conclusions drawn from the generic analysis are demonstrated for the ABC model by explicit calculation of its Landau expansion.