A Worm Algorithm for Two-Dimensional Spin Glasses

TL;DR

This paper introduces a worm algorithm for 2D spin glasses that efficiently samples low-temperature configurations by manipulating strings connecting frustrated plaquettes, outperforming traditional methods especially with free boundary conditions.

Contribution

The paper presents a novel worm algorithm based on low-temperature expansion for 2D spin glasses, demonstrating improved efficiency over existing algorithms.

Findings

Worm algorithm is as efficient as cluster or replica-exchange algorithms.

Algorithm is more efficient with free boundary conditions.

Accurate low-temperature specific heat data consistent with theoretical predictions.

Abstract

A worm algorithm is proposed for the two-dimensional spin glasses. The method is based on a low-temperature expansion of the partition function. The low-temperature configurations of the spin glass on square lattice can be viewed as strings connecting pairs of frustrated plaquettes. The worm algorithm directly manipulates these strings. It is shown that the worm algorithm is as efficient as any other types of cluster or replica-exchange algorithms. The worm algorithm is even more efficient if free boundary conditions are used. We obtain accurate low-temperature specific heat data consistent with a form c = T^{-2} exp(-2J/(k_BT)), where T is temperature and J is coupling constant, for the +/-J two-dimensional spin glass.