Further extensions of the high-temperature expansions for the two-dimensional classical XY model on the triangular and the square lattices

Source: arXiv

ABSTRACT The high-temperature expansions for the spin-spin correlation function of the two-dimensional classical XY (planar rotator) model are extended by two terms, from order 24 through order 26, in the case of the square lattice, and by five terms, from order 15 through order 20, in the case of the triangular lattice. The data are analyzed to improve the current estimates of the critical parameters of the models.

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    ABSTRACT: We study the classical XY (plane rotator) model at the Kosterlitz-Thouless phase transition. We simulate the model using the single cluster algorithm on square lattices of a linear size up to L=2048.We derive the finite size behaviour of the second moment correlation length over the lattice size xi_{2nd}/L at the transition temperature. This new prediction and the analogous one for the helicity modulus are confronted with our Monte Carlo data. This way beta_{KT}=1.1199 is confirmed as inverse transition temperature. Finally we address the puzzle of logarithmic corrections of the magnetic susceptibility chi at the transition temperature. Comment: Monte Carlo results for xi/L in table 1 and 2 corrected. Due to a programming error,these numbers were wrong by about a factor 1+1/L^2. Correspondingly the fits with L_min=64 and 128 given in table 5 and 6 are changed by little.The central results of the paper are not affected. Wrong sign in eq.(52) corrected. Appendix extended
    Journal of Physics A General Physics 02/2005;
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    ABSTRACT: The massive continuum limit of the (1+1)-dimensional O(2) nonlinear σ-model (XY-model) is studied using its equivalence to the sine-Gordon model at its asymptotically free point. It is shown that leading lattice artifacts are universal but they vanish only as inverse powers of the logarithm of the correlation length. Such leading artifacts are calculated for the case of the scattering phase shifts and the correlation function of the Noether current using the bootstrap S-matrix and perturbation theory respectively.
    Journal of Physics A General Physics 06/2001; 34(25):5237.

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