Critical behavior of the compact 3D U(1) gauge theory at finite temperature

Critical properties of the compact three-dimensional U(1) lattice gauge theory are explored atfinite temperatures. The critical point of the deconfinement phase transition, critical indices and the string tension are studied numerically on lattices with temporal extension Nt = 8 and spatialextension ranging from L = 32 to L = 256. The critical indices, which govern the behaviouracross the deconfinement phase transition, are generally expected to coincide with the criticalindices of the two-dimensional XY model. It is found that the determination of the infinite volumecritical point differs from the pseudo-critical coupling at L =32, found earlier in the literature andimplicitly assumed as the onset value of the deconfined phase. The critical index u computed from the scaling of the pseudocritical couplings agrees well with the value u = 1/2 of the XY model.The computation of the index eta brings to a value larger than expected. The possible reasons forsuch behaviour are discussed.