Critical behavior of the compact 3D U(1) theory in the limit of zero spatial coupling

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 Nt = 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.