Derivation of the Fradkin-Shenker result from duality: Links to spin systems in external magnetic fields and percolation crossovers

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 percolation crossover line in the two-dimensional Z₂/Z₂ theory.