Monte Carlo analysis of the two-dimensional<i>XY</i>model. II. Comparison with the Kosterlitz renormalization-group equations

Abstract

The temperature scale of relevance for the vortex excitations in the two-dimensional XY model is identified. The size dependence of the helicity modulus at constant vortex temperature is then obtained by Monte Carlo simulations. The Monte Carlo data are then compared with the results for the length-dependent dielectric function from the Kosterlitz renormalization-group equations. The agreement is excellent for temperatures up to and slightly above ${\mathit{T}}_{\mathit{c}}$. The critical temperature is determined to be ${\mathit{T}}_{\mathit{c}}$=0.892 13(10). The temperature dependence of the characteristic length right above ${\mathit{T}}_{\mathit{c}}$ is also obtained and found to be in agreement with recent results from high-temperature series expansions.