Ensemble Inequivalence in the Spherical Spin Glass Model with Nonlinear Interactions

TL;DR

This paper studies the phenomenon of ensemble inequivalence in a spherical spin glass model with nonlinear polynomial interactions, revealing first-order phase transitions and ensemble-dependent behaviors such as negative specific heat.

Contribution

It provides an exact solution for the model with arbitrary polynomial order and characterizes ensemble inequivalence and phase transition properties.

Findings

First-order phase transitions occur for p ≥ 5.

Ensemble dependence leads to negative specific heat in the microcanonical ensemble.

Phase behavior varies depending on the statistical ensemble used.

Abstract

We investigate the ensemble inequivalence of the spherical spin glass model with nonlinear interactions of polynomial order $p$. This model is solved exactly for arbitrary $p$ and is shown to have first-order phase transitions between the paramagnetic and spin glass or ferromagnetic phases for $p \geq 5$. In the parameter region around the first-order transitions, the solutions give different results depending on the ensemble used for the analysis. In particular, we observe that the microcanonical specific heat can be negative and the phase may not be uniquely determined by the temperature.