A 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 crossover line in the two dimensional Z2/Z2 theory. 
Zohar Nussinov