CRITICAL-BEHAVIOR OF THE 2-DIMENSIONAL XY MODEL

We present detailed Monte Carlo results for the susceptibility chi, correlation length xi, and specific heat C(upsilon) 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 less-than-or-equal-to T less-than-or-equal-to 1.43 corresponding to 2 < xi < 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 v = 0.5 and eta = 0.25. Our best estimate, T(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 almost-equal-to 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.