The ground state energy of the Edwards-Anderson spin glass model with a parallel tempering Monte Carlo algorithm

TL;DR

This paper evaluates the efficiency of a parallel tempering Monte Carlo method in finding ground states of the Edwards-Anderson spin glass model across different dimensions and distributions, providing a simple parameter estimation formula.

Contribution

It introduces a systematic analysis and a simple formula for parameter estimation in parallel tempering, improving ground state search efficiency for spin glasses.

Findings

The method achieves ground state energies consistent with literature.

Performance is comparable to other advanced heuristics.

A formula for optimal parameter selection was derived.

Abstract

We study the efficiency of parallel tempering Monte Carlo technique for calculating true ground states of the Edwards-Anderson spin glass model. Bimodal and Gaussian bond distributions were considered in two and three-dimensional lattices. By a systematic analysis we find a simple formula to estimate the values of the parameters needed in the algorithm to find the GS with a fixed average probability. We also study the performance of the algorithm for single samples, quantifying the difference between samples where the GS is hard, or easy, to find. The GS energies we obtain are in good agreement with the values found in the literature. Our results show that the performance of the parallel tempering technique is comparable to more powerful heuristics developed to find the ground state of Ising spin glass systems.