Phase structure of 3D Z (N) lattice gauge theories at finite temperature

We perform a numerical study of the phase transitions in three-dimensional Z (N) lattice gauge theories at finite temperature for N > 4. Using the dual formulation of the models and a cluster algorithm we locate the position of the critical points and study the critical behavior across both phase transitions in details. In particular, we determine various critical indices, compute the average action and the specific heat. Our results are consistent with the two transitions being of infinite order. Furthermore, they belong to the universality class of two-dimensional Z (N) vector spin models.