A gauge invariant cluster algorithm for the Ising spin glass

TL;DR

This paper introduces a gauge invariant cluster algorithm for the 2D Ising spin glass, enabling efficient simulations near critical points by respecting gauge symmetry and accurately calculating properties like specific heat.

Contribution

A novel gauge invariant cluster algorithm for the 2D Ising spin glass that improves simulation efficiency near criticality by respecting gauge symmetry.

Findings

Exact ground state energy computed using Edmond's algorithm.

The new algorithm effectively studies specific heat near criticality.

Gauge invariance ensures consistent treatment of equivalent spin glasses.

Abstract

The frustrated Ising model in two dimensions is revisited. The frustration is quantified in terms of the number of non-trivial plaquettes which is invariant under the Nishimori gauge symmetry. The exact ground state energy is calculated using Edmond's algorithm. A novel cluster algorithm is designed which treats gauge equivalent spin glasses on equal footing and allows for efficient simulations near criticality. As a first application, the specific heat near criticality is investigated.