Logarithmic Corrections in the 2D XY Model

Abstract

Using two sets of high-precision Monte Carlo data for the two-dimensional XY model in the Villain formulation on square $L \times L$ 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 $512^2$ we obtain $r = -0.0270(10)$, in agreement with recent work of Kenna and Irving on the the finite-size scaling of Lee-Yang zeros in the cosine formulation of the XY model. By studying susceptibilities and correlation lengths up to $ξ\approx 140$ 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.