Many-body spin glasses in the microcanonical ensemble

TL;DR

This paper studies the p-spin spin glass model in the microcanonical ensemble, revealing ensemble inequivalence and phase transition differences for p > 2, extending understanding of long-range interacting disordered systems.

Contribution

It provides the first systematic analysis of long-range spin glasses in the microcanonical ensemble, highlighting differences from the canonical ensemble for p > 2.

Findings

For p=2, microcanonical results match canonical results with second-order transitions.

For p>2, the transition is first order and ensembles differ.

Ensemble inequivalence is demonstrated in the limit p→infinity.

Abstract

We investigate the p-spin model with Gaussian-distributed random interactions in the microcanonical ensemble using the replica theory. For p=2, there are only second-order phase transitions and we recover the results of Sherrington and Kirkpatrick obtained in the canonical ensemble. For p > 2, the transition between the ferromagnetic and paramagnetic phases is of first order, and the microcanonical and canonical ensembles give different results. We also discuss the ensemble inequivalence of the random energy model, corresponding to the limit p => infinity. This is the first systematic treatment of spin glasses with long-range interactions in the microcanonical ensemble, which shows how the two ensembles give different results.