  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 N_t=8 on lattices with spatial extension ranging from L=32 to L=256. Our
determination of the infinite volume critical point on the lattice with N_t=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 $\nu$ computed from the scaling of the
pseudo-critical couplings with the extension of the spatial lattice agrees well
with the XY value $\nu$=1/2. On the other hand, the index $\eta$ shows large
deviation from the expected universal value. The possible reasons of such
behavior are discussed in details.
