Logarithmic Corrections in the 2D XY Model

Details Logarithmic Corrections in the 2D XY Model Logarithmic Corrections in the 2D XY Model

1996-09-28

arxiv.org/abs/hep-lat/9609045v1

Physics

High Energy Physics

High Energy Physics - Lattice

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

Scientific paper

10.1103/PhysRevB.55.3580

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 $(ln L)^{-2r}$ 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.

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