Lattice gauge theory and a random-medium Ising model

TL;DR

This paper explores the connection between lattice gauge theories and statistical models like the Ising and Potts models, showing how linearized gauge theories relate to random-weighted Ising models and introducing new observables.

Contribution

It establishes a novel equivalence between linearized Abelian gauge theory and a random-weighted Ising model, and extends this relation to Yang-Mills and Potts models, introducing new observables.

Findings

Linearized Abelian gauge theory expectation matches Ising model with random edge-weights.

Relation between Yang-Mills theory and 4-state Potts model is demonstrated.

A new observable for the Potts model is introduced.

Abstract

We study linearization of lattice gauge theory. Linearized theory approximates lattice gauge theory in the same manner as the loop O(n)-model approximates the spin O(n)-model. Under mild assumptions, we show that the expectation of an observable in linearized Abelian gauge theory coincides with the expectation in the Ising model with random edge-weights. We find a similar relation between Yang-Mills theory and 4-state Potts model. For the latter, we introduce a new observable.