Critical behavior of the two-dimensional XY model

We present detailed Monte Carlo results for the susceptibility χ, correlation length ξ, and specific heat ${\mathit{C}}_{\mathit{v}}$ for the XY model. The simulations are done on ${64}^2$, ${128}^2$, ${256}^2$, and ${512}^2$ 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, ${\mathit{T}}_{\mathit{c}}$=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.