A Derivation of the Fradkin-Shenker Result From Duality: Links to Spin Systems in External Magnetic Fields and Percolation Crossovers

TL;DR

This paper provides a rigorous derivation of the Fradkin-Shenker phase diagram for gauge theories with matter, using duality and Lee-Yang theorems, and explores related spin systems and percolation phenomena.

Contribution

It offers a new proof of the Fradkin-Shenker result through duality and extends the analysis to two-dimensional Z2/Z2 theories, establishing a sharp crossover line.

Findings

Rigorous proof of the Fradkin-Shenker phase diagram

Identification of a sharp crossover line in 2D Z2/Z2 theory

Connections between gauge theories, spin systems, and percolation

Abstract

In this article, we illustrate how the qualitative phase diagram of a gauge theory coupled to matter can be directly proved and how rigorous numerical bounds may be established. Our work reaffirms the seminal result of Fradkin and Shenker from another vista. Our main ingredient is the combined use of the self-duality of the three dimensional Z2/Z2 theory and an extended Lee-Yang theorem. We comment on extensions of these ideas and firmly establish the existence of a sharp crossover line in the two dimensional Z2/Z2 theory.