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 L3L lattices, the scaling behavior of the susceptibility x and correlation length j at the Kosterlitz-Thouless phase transition is analyzed with emphasis on multiplicative logarithmic corrections (lnL) in the finite-size scaling region and (lnj) in the high-temperature phase near criticality, respectively. By analyzing the susceptibility at criticality on lattices of size up to 512 we obtain r5 20.0270(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 j'140 in the high-temperature phase, however, we arrive at quite a different estimate of r50.0560(17), which is in good agreement with recent analyses of thermodynamic Monte Carlo data and high-temperature series expansions of the cosine formulation. @S0163-1829~97!00305-6#