Ensemble Inequivalence and the Spin-Glass Transition

TL;DR

This paper investigates how the phase transition in a many-body spin-glass model with integer spins differs between microcanonical and canonical ensembles, revealing ensemble inequivalence and deriving key phase transition lines.

Contribution

It introduces an exactly solvable integer-spin spin-glass model and extends the understanding of ensemble inequivalence and phase transition lines in such systems.

Findings

First-order phase transition depends on ensemble choice

Exact solution of the integer-spin model in the infinite interaction limit

Derivation of the integer-spin de Almeida-Thouless line

Abstract

We report on the ensemble inequivalence in a many-body spin-glass model with integer spin. The spin-glass phase transition is of first order for certain values of the crystal field strength and is dependent whether it was derived in the microcanonical or the canonical ensemble. In the limit of infinitely many-body interactions, the model is the integer-spin equivalent of the random-energy model, and is solved exactly. We also derive the integer-spin equivalent of the de Almeida-Thouless line.