Proposal of a Checking Parameter in the Simulated Annealing Method Applied to the Spin Glass Model

TL;DR

This paper introduces a new checking parameter based on the Jarzynski equality to detect global minima in simulated annealing, enhancing the evaluation of annealing schedules in spin glass models.

Contribution

A novel checking parameter utilizing the Jarzynski equality is proposed to assess the effectiveness of simulated annealing in finding global minima.

Findings

The parameter detects when the system is in a global minimum.

Application to +-J and Gaussian Ising spin glass models demonstrates its effectiveness.

Monte Carlo simulations confirm the parameter's utility in identifying trapped states.

Abstract

We propose a checking parameter utilizing the breaking of the Jarzynski equality in the simulated annealing method using the Monte Carlo method. This parameter is based on the Jarzynski equality. By using this parameter, to detect that the system is in global minima of the free energy under gradual temperature reduction is possible. Thus, by using this parameter, one is able to investigate the efficiency of annealing schedules. We apply this parameter to the +-J Ising spin glass model. The application to the Gaussian Ising spin glass model is also mentioned. We discuss that the breaking of the Jarzynski equality is induced by the system being trapped in local minima of the free energy. By performing Monte Carlo simulations of the +-J Ising spin glass model and a glassy spin model proposed by Newman and Moore, we show the efficiency of the use of this parameter.