Phase transitions in Thirring's model

TL;DR

This paper provides a comprehensive analysis of Thirring's model, revealing phase transitions, ensemble inequivalence, and the relationship between microcanonical and canonical critical points, serving as a prototype for long-range interacting systems.

Contribution

It offers the first complete phase diagram of Thirring's model in both ensembles and analytically relates the critical points, highlighting ensemble inequivalence and long-range interaction effects.

Findings

Line of first-order phase transitions ending in a critical point

Ensemble inequivalence with different phase diagram features

Analytical relation between microcanonical and canonical critical points

Abstract

In his pioneering work on negative specific heat, Walter Thirring in\-tro\-duced a model that is solvable in the microcanonical ensemble. Here, we give a complete description of the phase-diagram of this model in both the microcanonical and the canonical ensemble, highlighting the main features of ensemble inequivalence. In both ensembles, we find a line of first-order phase transitions which ends in a critical point. However, neither the line nor the point have the same location in the phase-diagram of the two ensembles. We also show that the microcanonical and canonical critical points can be analytically related to each other using a Landau expansion of entropy and free energy, respectively, in analogy with what has been done in [O. Cohen, D. Mukamel, J. Stat. Mech., P12017 (2012)]. Examples of systems with certain symmetries restricting the Landau expansion have been considered in this reference, while no such restrictions are present in Thirring's model. This leads to a phase diagram that can be seen as a prototype for what happens in systems of particles with kinematic degrees of freedom dominated by long-range interactions.