Hysteretic optimization for the Sherrington-Kirkpatrick spin glass

TL;DR

This paper demonstrates that hysteretic optimization effectively finds ground states in large Sherrington-Kirkpatrick spin glass systems, providing new insights into energy distribution convergence and error estimation.

Contribution

It introduces hysteretic optimization as a powerful heuristic for spin glass ground state determination and offers a novel error estimation approach applicable to other methods.

Findings

Effective for systems up to 2000 spins

Faster convergence of energy distribution than previously thought

Provides a useful error estimation technique

Abstract

Hysteretic optimization is a heuristic optimization method based on the observation that magnetic samples are driven into a low energy state when demagnetized by an oscillating magnetic field of decreasing amplitude. We show that hysteretic optimization is very good for finding ground states of Sherrington-Kirkpatrick spin glass systems. With this method it is possible to get good statistics for ground state energies for large samples of systems consisting of up to about 2000 spins. The way we estimate error rates may be useful for some other optimization methods as well. Our results show that both the average and the width of the ground state energy distribution converges faster with increasing size than expected from earlier studies.