Critical behavior of the planar magnet model in three dimensions

We study the critical behavior of the three-dimensional planar magnet model in which each spin is considered to have three components of which only th e x and y components are coupled. We use a hybrid Monte Carlo algorithm in which a single-cluster update is combined with the over-relaxation and Metr opolis spin reorientation algorithm. Periodic boundary conditions were appl ied in all directions. We have calculated the fourth-order cumulant in fini te-size lattices using the single-histogram reweighting method. Using finit e-size scaling theory, we obtained the critical temperature which is very d ifferent from that of the usual XY model. At the critical temperature, we c alculated the susceptibility and the magnetization on lattices of size up t o 423 Using finite-size scaling theory we accurately determine the critical exponents of the model and find that nu=0.670(7), gamma/nu=1.9696(37), and beta/nu=0.515(2). Thus we conclude that the model belongs to the same univ ersality class with the XY model, as expected. [S0163-1829(99)07117-9].