Microcanonical Analysis of Spin Glasses Using Gauge Symmetry

TL;DR

This paper uses gauge transformations to analyze spin glasses in the microcanonical ensemble, demonstrating ensemble equivalence on the Nishimori line and exploring conditions for inequivalence away from it, with implications for long-range interactions.

Contribution

It proves that results on the Nishimori line are consistent between ensembles and establishes conditions for ensemble inequivalence in spin glasses with quenched disorder.

Findings

Ensemble equivalence holds on the Nishimori line for finite systems.

Results derived under the canonical ensemble are reproducible microcanonically on the NL.

Ensemble inequivalence may occur away from the NL in systems with long-range interactions.

Abstract

We apply the method of gauge transformation to spin glasses under the microcanonical ensemble to study the possibility of ensemble inequivalence in systems with long-range interactions and quenched disorder. It is proved that all the results derived under the canonical ensemble on the Nishimori line (NL) can be reproduced by the microcanonical ensemble irrespective of the range of interactions. This establishes that ensemble inequivalence should take place away from the NL if it happens in spin glasses. It is also proved on the NL that the microcanonical configurational average of the energy as a function of temperature is exactly equal to the average energy in the canonical ensemble for any finite-size systems with Gaussian disorder. In this sense, ensembles are equivalent even for finite systems.