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 $\chi$ and correlation length $\xi$ at the Kosterlitz-Thouless phase transition is analyzed with emphasis on multiplicative logarithmic corrections $(lnL{)}^{-2r}$ in the finite-size scaling region and $(ln\xi {)}^{-2r}$ 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 $\xi \approx 140$ 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.

13 pages, LaTeX + 8 postscript figures. See also http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.html

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