Simple spin models with non-concave entropies

TL;DR

This paper investigates two simple spin models demonstrating that microcanonical entropy can be non-concave and that microcanonical and canonical ensembles may yield different descriptions in the thermodynamic limit.

Contribution

It introduces and solves two simple spin models showing non-concave entropies and ensemble inequivalence, expanding understanding of statistical mechanics.

Findings

Microcanonical entropy can be non-concave.

Ensemble inequivalence occurs in these models.

Models are analytically solvable.

Abstract

Two simple spin models are studied to show that the microcanonical entropy can be a non-concave function of the energy, and that the microcanonical and canonical ensembles can give non-equivalent descriptions of the same system in the thermodynamic limit. The two models are simple variations of the classical paramagnetic spin model of non-interacting spins and are solved as easily as the latter model.