Variant actions and phase structure in lattice gauge theory

We study a simple generalization of Wilson's SU(2) lattice gauge theory. In various limits the model reduces to the usual SU(2), SO(3), or $Z_2$ models. Using Monte Carlo techniques on a four-dimensional lattice, we follow the known SO(3) and $Z_2$ first-order transitions into the phase diagram. They merge at a triple point and continue together to a critical end point. The peak in the specific heat of the SU(2) model is a shadow of this nearby singularity.