Logarithmic corrections in the two-dimensional XY model

Using two sets of high-precision Monte Carlo data for the two-dimensional XY model in the Villain formulation on square L×{}L lattices, the scaling behavior of the susceptibility {χ} and correlation length {ξ} at the Kosterlitz-Thouless phase transition is analyzed with emphasis on multiplicative logarithmic corrections (ln L)^-2r in the finite-size scaling region and (ln {ξ})^-2r in the high-temperature phase near criticality, respectively. By analyzing the susceptibility at criticality on lattices of size up to 512² we obtain r=-0.0270(10), in agreement with recent work of Kenna and Irving on the finite-size scaling of Lee-Yang zeros in the cosine formulation of the XY model. By studying susceptibilities and correlation lengths up to {ξ}{≈}140 in the high-temperature phase, however, we arrive at quite a different estimate of r=0.0560(17), which is in good agreement with recent analyses of thermodynamic Monte Carlo data and high-temperature series expansions of the cosine formulation.