We investigate the critical properties of the two-dimensional Z(5) vector model. For this purpose, we propose a cluster algorithm, valid for Z(N) models with odd values of N. The two-dimensional Z(5) vector model is conjectured to exhibit two phase transitions with a massless intermediate phase. 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 and compare the results with analytical predictions.

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.

Critical properties of the compact three-dimensional U (1) lattice gauge theory are explored at finite temperatures on an asymmetric lattice. For vanishing value of the spatial gauge coupling one obtains an effective twodimensional spin model which describes the interaction between Polyakov loops. We study numerically the effective spin model for N t = 1, 4, 8 on lattices with spatial extent ranging from L = 64 to 256. Our results indicate that the finite temperature U (1) lattice gauge theory belongs to the universality class of the two-dimensional XY model, thus supporting the Svetitsky-Yaffe conjecture.