Critical behavior of the compact 3DU(1) gauge theory on isotropic lattices

Abstract

We report on the computation of the critical point of the deconfinement phasetransition, critical indices and the string tension in the compact three-dimensionalU(1) lattice gauge theory at finite temperatures. The critical indices govern thebehavior across the deconfinement phase transition in the pure gaugeU(1) model and are generally expected to coincide with the critical indices of the two-dimensionalXY model. We studiednumerically the U(1) model for Nt = 8 on lattices with spatial extension ranging fromL = 32 to 256. Our determination of the infinite volume critical point on the lattice withNt = 8 differs substantially from the pseudo-critical coupling atL = 32, foundearlier in the literature and implicitly assumed as the onset value of the deconfined phase. The critical indexν computedfrom the scaling of the pseudo-critical couplings with the extension of the spatial lattice agrees well with theXY valueν = 1/2. On the otherhand, the index η shows large deviation from the expected universal value. The possible reasons for suchbehavior are discussed in detail.