Matching Kasteleyn Cities for Spin Glass Ground States

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.

4 pages, 2 figures; minor clarifications

References in corpus (3)

• Absence of an Almeida-Thouless line in Three-Dimensional Spin Glasses
• Are Domain Walls in Spin Glasses Described by Stochastic Loewner Evolutions?
• Energy size effects of two-dimensional Ising spin glasses

Cited by in corpus (3)

• Efficient Exact Inference in Planar Ising Models
• Exact Algorithm for Sampling the 2D Ising Spin Glass
• Persistence and Memory in Patchwork Dynamics for Glassy Models