Transition of Z2 gauge theory in four dimensions

Question

Are there rigorous results (apart from the self-duality of the system and its self-dual transition point) concerning the character of the transition of the Ising lattice gauge theory in four dimensions?

Answer 1

The latest result on the model is by Malin Forsström:

"Decay of correlations in finite Abelian lattice gauge theories"

which applies to finite Abelian gauge groups and in particular $\mathbb{Z}/2\mathbb{Z}$. It proves exponential decay of two point functions in some regime with regards to the coupling ($\beta\ge 0.4$ if I understood correctly). To review the literature on rigorous results for Wegner's Ising discrete lattice gauge theory, one can look at the references in the article by Forsström, in particular the ones by Fröhlich-Spencer, Borgs and Chatterjee. One can also start with the article by Fröhlich-Spencer (covers $\mathbb{Z}/N\mathbb{Z}$ with $N$ large) and look up papers which cite it on say Google Scholar.