Matching Kasteleyn Cities for Spin Glass Ground States

TL;DR

This paper introduces a fast optimization algorithm combining Pfaffian and matching methods to efficiently compute ground states of 2D Ising spin glasses, overcoming slow dynamics in these materials.

Contribution

It presents a novel, efficient method for finding exact ground states of 2D spin glasses by integrating Kasteleyn cities with Pfaffian and matching techniques.

Findings

Accurate ground state energy densities for 2D Ising spin glasses.

Algorithm efficiently strips droplet excitations from excited states.

Applicable to systems with complex boundary conditions.

Abstract

As spin glass materials have extremely slow dynamics, devious numerical methods are needed to study low-temperature states. A simple and fast optimization version of the classical Kasteleyn treatment of the Ising model is described and applied to two-dimensional Ising spin glasses. The algorithm combines the Pfaffian and matching approaches to directly strip droplet excitations from an excited state. Extended ground states in Ising spin glasses on a torus, which are optimized over all boundary conditions, are used to compute precise values for ground state energy densities.