Exact Results for the Jarzynski Equality in Ising Spin Glass Models Derived by Using a Gauge Symmetry

TL;DR

This paper derives exact results for the Jarzynski equality in Ising spin glass models using gauge symmetry, providing bounds and relations for work exponentials across different phases and configurations.

Contribution

It introduces a novel application of gauge symmetry to obtain exact bounds and relations for the Jarzynski equality in spin glass models, including the +-J and Gaussian models.

Findings

Derived exact lower bounds of exponentiated work for ferromagnetic phases and multicritical points.

Established rigorous relations between exponentiated work for different quenched configurations.

Obtained exact exponentiated work for the spin glass phase in Gaussian models.

Abstract

Exact results for the Jarzynski equality are derived for Ising spin glass models. The Jarzynski equality is an equality that connects the work in nonequilibrium and the difference between free energies. The work is performed in switching an external parameter of the system. As the Ising spin glass models, the +-J model and the Gaussian model are investigated. For the +-J model and the Gaussian model, we derive exact lower bounds of the exponentiated work for investigating the ferromagnetic phases and the multicritical points, and derive rigorous relations between the exponentiated work which have different quenched random configurations. For the Gaussian model, we derive the exact exponentiated work for investigating the spin glass phase. Exact results for the infinite-range models are also obtained. The present results are obtained by using a gauge symmetry, and are related to points on the Nishimori lines which are special lines in the phase diagrams. The present results do not depend on any lattice shape, and a part of the present results instead depends on the number of nearest-neighbor pairs in the whole system.