Classification of phase transitions and ensemble inequivalence, in systems with long range interactions

TL;DR

This paper classifies phase transitions and ensemble inequivalence in systems with long-range interactions, highlighting their unique behaviors and linking microcanonical and canonical ensemble phenomena.

Contribution

It introduces a systematic classification of microcanonical phase transitions and their relation to canonical ones in non-additive long-range interacting systems.

Findings

Microcanonical ensemble can exhibit richer behavior than canonical.

Identification of generic situations of ensemble inequivalence.

Discussion of observed and potential phase transitions in specific systems.

Abstract

Systems with long range interactions in general are not additive, which can lead to an inequivalence of the microcanonical and canonical ensembles. The microcanonical ensemble may show richer behavior than the canonical one, including negative specific heats and other non-common behaviors. We propose a classification of microcanonical phase transitions, of their link to canonical ones, and of the possible situations of ensemble inequivalence. We discuss previously observed phase transitions and inequivalence in self-gravitating, two-dimensional fluid dynamics and non-neutral plasmas. We note a number of generic situations that have not yet been observed in such systems.