Critical behavior of the two-dimensional XY model

We present detailed Monte Carlo results for the susceptibility {chi}, correlation length {xi}, and specific heat {ital C}{sub {ital v}} for the {ital XY} model. The simulations are done on 64{sup 2}, 128{sup 2}, 256{sup 2}, and 512{sup 2} lattices over the temperature range 0.98{le}{ital T}{le}1.43 corresponding to 2{lt}{xi}{lt}70. Fits to {chi} and {xi} data favor a Kosterlitz-Thouless (KT) singularity over a second-order transition; however, unconstrained four-parameter KT fits do not confirm the predicted values {nu}=0.5 and {eta}=0.25. Our best estimate, {ital T}{sub {ital c}}=0.894(5), is obtained using KT fits with {nu} fixed at 0.5. The exponent {eta} 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 {eta}{approx}0.235 at {ital 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.