Ensemble Inequivalence in Ising Chains with Competing Interactions

TL;DR

This paper investigates how competing interactions in a one-dimensional Ising model cause differences in phase behavior between microcanonical and canonical ensembles, revealing complex phase diagrams and novel critical points.

Contribution

It introduces a simple yet rich Ising chain model with competing interactions, demonstrating ensemble inequivalence and identifying new critical phenomena.

Findings

Ensemble inequivalence occurs at lower temperatures and larger coupling magnitudes.

The microcanonical ensemble exhibits additional critical and triple points.

A fourth-order critical point is characterized via Landau theory.

Abstract

We study the effect of competing interactions on ensemble inequivalence. We consider a one-dimensional Ising model with ferromagnetic mean-field interactions and short-range nearest-neighbor and next-nearest-neighbor couplings which can be either ferromagnetic or antiferromagnetic. Despite the relative simplicity of the model, our calculations in the microcanonical ensemble reveal a rich phase diagram. The comparison with the corresponding phase diagram in the canonical ensemble shows the presence of phase transition points and lines which are different in the two ensembles. As an example, in a region of the phase diagram where the canonical ensemble shows a critical point and a critical end point, the microcanonical ensemble has an additional critical point and also a triple point. The regions of ensemble inequivalence typically occur at lower temperatures and at larger absolute values of the competing couplings. The presence of two free parameters in the model allows us to obtain a fourth-order critical point, which can be fully characterized by deriving its Landau normal form.