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

Abstract

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 two-dimensional 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 extension ranging from L=64 to L=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.

17 pages, 5 figures; two references added, a few comments included, title changed; version to appear on J. Stat. Mech