Vortex characterisation of frustration in the 2d Ising spin glass

TL;DR

This paper explores how vortex configurations relate to frustration in the 2D Ising spin glass, revealing gauge symmetries and providing a polynomial-time method to compute ground state energies.

Contribution

It introduces a gauge-invariant vortex framework and demonstrates an efficient algorithm for calculating ground state energies in the 2D Ising spin glass.

Findings

Partition function depends only on vortex distribution

Gauge symmetry relates different frustration configurations

Ground state energy computable in polynomial time

Abstract

The frustrated Ising model on a two-dimensional lattice with open boundary conditions is revisited. A hidden Z2 gauge symmetry relates models with different frustrations which, however, share the same partition function. By means of a duality transformation, it is shown that the partition function only depends on the distribution of gauge invariant vortices on the lattice. We finally show that the exact ground state energy can be calculated in polynomial time using Edmonds' algorithm.