Efficient Cluster Algorithm for Spin Glasses in Any Space Dimension

TL;DR

This paper introduces a novel cluster algorithm for Ising spin glasses applicable in any dimension, significantly accelerating thermalization and outperforming existing methods, especially in complex topologies like chimera.

Contribution

The authors develop a universal isoenergetic cluster algorithm for spin glasses that enhances simulation efficiency across all spatial dimensions.

Findings

Speeds up thermalization by over tenfold at difficult temperatures.

Effective in 2D, 3D, and nonplanar chimera topologies.

Outperforms conventional methods with increasing system size.

Abstract

Spin systems with frustration and disorder are notoriously difficult to study both analytically and numerically. While the simulation of ferromagnetic statistical mechanical models benefits greatly from cluster algorithms, these accelerated dynamics methods remain elusive for generic spin-glass-like systems. Here we present a cluster algorithm for Ising spin glasses that works in any space dimension and speeds up thermalization by at least one order of magnitude at temperatures where thermalization is typically difficult. Our isoenergetic cluster moves are based on the Houdayer cluster algorithm for two-dimensional spin glasses and lead to a speedup over conventional state-of-the-art methods that increases with the system size. We illustrate the benefits of the isoenergetic cluster moves in two and three space dimensions, as well as the nonplanar chimera topology found in the D-Wave Inc.~quantum annealing machine.