Improved extremal optimization for the Ising spin glass

TL;DR

This paper introduces an improved extremal optimization algorithm for 2D and 3D spin glasses, significantly increasing the speed of finding exact ground states, especially for larger systems, thus aiding the study of disordered materials.

Contribution

The paper presents a novel adaptive extremal optimization variant that reduces redundant flips, achieving much faster ground state computations for spin glasses.

Findings

Speed-up of about 10^4 for 16x16 systems

Speed-up of about 10^2 for 8x8x8 systems

Rapid increase in efficiency with system size

Abstract

A version of the extremal optimization (EO) algorithm introduced by Boettcher and Percus is tested on 2D and 3D spin glasses with Gaussian disorder. EO preferentially flips spins that are locally ``unfit''; the variant introduced here reduces the probability to flip previously selected spins. Relative to EO, this adaptive algorithm finds exact ground states with a speed-up of order $10^{4}$ ($10^{2}$) for $16^{2}$- ($8^{3}$-) spin samples. This speed-up increases rapidly with system size, making this heuristic a useful tool in the study of materials with quenched disorder.