Ensemble inequivalence in a mean-field XY model with ferromagnetic and nematic couplings

TL;DR

This paper investigates ensemble inequivalence in a long-range XY spin model with mixed ferromagnetic and nematic interactions, revealing discrepancies between microcanonical and canonical phase diagrams, especially near first-order transitions.

Contribution

It demonstrates ensemble inequivalence in a mean-field XY model with combined ferromagnetic and nematic couplings through phase diagram mapping.

Findings

Microcanonical and canonical phase diagrams differ significantly.

Temperature jumps occur at first-order transitions.

Coexistence and forbidden regions are identified in phase diagrams.

Abstract

We explore ensemble inequivalence in long-range interacting systems by studying an XY model of classical spins with ferromagnetic and nematic coupling. We demonstrate the inequivalence by mapping the microcanonical phase diagram onto the canonical one, and also by doing the inverse mapping. We show that the equilibrium phase diagrams within the two ensembles strongly disagree within the regions of first-order transitions, exhibiting interesting features like temperature jumps. In particular, we discuss the coexistence and forbidden regions of different macroscopic states in both the phase diagrams.