Monte Carlo study of Abelian lattice gauge theories

Using Monte Carlo techniques, we study the thermodynamics of four-dimensional Euclidean lattice gauge theories, with gauge groups $Z_N$ and U(1). For $N\le 4$ the models exhibit a single first-order phase transition, while for $N\ge 5$ we observe two transitions of higher order. As $N$ increases, one of these transitions moves toward zero temperature, whereas the other remains at finite temperature and survives in the U(1) limit. The behavior of the Wilson loop factor is also analyzed for the $Z_2$ and $Z_6$ models.