Phase transitions in Thirring's model

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.

16 pages, 6 figures

References in corpus (2)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Solvable model of a self-gravitating system

Cited by in corpus (8)

• Complete analysis of ensemble inequivalence in the Blume-Emery-Griffiths model
• Long-range interacting systems in the unconstrained ensemble
• Concavity, Response Functions and Replica Energy
• Microcanonical characterization of first-order phase transitions in a generalized model for aggregation
• Shape-free theory for the self-assembly kinetics in macromolecular systems
• Phase transitions in the unconstrained ensemble
• Lifetime of locally stable states near a phase transition in the Thirring model
• Modified Thirring model beyond the excluded-volume approximation