Phase space gaps and ergodicity breaking in systems with long range interactions

TL;DR

This paper investigates a generalized XY-model with mean-field interactions, revealing phase space gaps and ergodicity breaking, leading to coexistence of ordered and disordered phases within the same energy regions.

Contribution

It introduces a solvable model exhibiting ergodicity breaking and phase coexistence, extending understanding of long-range interacting systems in the microcanonical ensemble.

Findings

Gaps in magnetization at fixed energy cause ergodicity breaking.

First order phase transitions between ferromagnetic and paramagnetic phases.

Existence of stable phases within regions typically associated with the opposite phase.

Abstract

We study a generalized isotropic XY-model which includes both two-spin and four-spin mean-field interactions. This model can be solved in the microcanonical ensemble. It is shown that in certain parameter regions the model exhibits gaps in the magnetization at fixed energy, resulting in ergodicity breaking. This phenomenon has previously been reported in anisotropic and discrete spin models. The entropy of the model is calculated and the microcanonical phase diagram is derived, showing the existence of first order phase transitions from the ferromagnetic to a paramagnetic disordered phase. It is found that ergodicity breaking takes place both in the ferromagnetic and the paramagnetic phases. As a consequence, the system can exhibit a stable ferromagnetic phase within the paramagnetic region, and conversely a disordered phase within the magnetically ordered region.