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

We report on the computation of the critical point of the deconfinement phase transition, critical indices and the string tension in the compact three-dimensional U(1) lattice gauge theory at finite temperatures. The critical indices govern the behavior across the deconfinement phase transition in the pure gauge U(1) model and are generally expected to coincide with the critical indices of the two-dimensional XY model. We studied numerically the U(1) model for Nt = 8 on lattices with spatial extension ranging from L = 32 to 256. Our determination of the infinite volume critical point on the lattice with Nt = 8 differs substantially from the pseudo-critical coupling at L = 32, found earlier in the literature and implicitly assumed as the onset value of the deconfined phase. The critical index ν computed from the scaling of the pseudocritical couplings with the extension of the spatial lattice agrees well with the XY value ν = 1/2. On the other hand, the index η shows large deviation from the expected universal value. The possible reasons for such behavior are discussed in detail.