Critical behavior of the two-dimensional XY model

We present detailed Monte Carlo results for the susceptibility χ, correlation length ξ, and specific heat Cv for the XY model. The simulations are done on 642, 1282, 2562, and 5122 lattices over the temperature range 0.98≤T≤1.43 corresponding to 2<ξ<70. Fits to χ and ξ data favor a Kosterlitz-Thouless (KT) singularity over a second-order transition; however, unconstrained four-parameter KT fits do not confirm the predicted values ν=0.5 and η=0.25. Our best estimate, Tc=0.894(5), is obtained using KT fits with ν fixed at 0.5. The exponent η is calculated as a function of temperature in the spin-wave phase using Monte Carlo renormalization-group and finite-size-scaling methods. Both methods give consistent results and we find η∼0.235 at T=0.894. We also present results for the behavior of vortex density across the transition and exhibit how the dilute-gas approximation breaks down