arXiv:0710.0338 · Physical Review B

High-temperature expansions through order 24 for the two-dimensional classical XY model on the square lattice

P. Butera, M. Pernici

Published Sep 26, 2007• 9 citations

Abstract

The high-temperature expansion of the spin-spin correlation function of the two-dimensional classical XY (planar rotator) model on the square lattice is extended by three terms, from order 21 through order 24, and analyzed to improve the estimates of the critical parameters.

DOI: 10.1103/physrevb.76.092406

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arXiv:0710.0338 · Physical Review B

High-temperature expansions through order 24 for the two-dimensional classical XY model on the square lattice

P. Butera, M. Pernici

Published Sep 26, 2007• 9 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.76.092406

Related papers

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

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arXiv:0806.1496Jun 9, 20080 citations

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arXiv:hep-lat/9305002Physical review. B, Condensed matterNov 1, 199315 citations

Quantitative study of the Kosterlitz-Thouless phase transition in anXYmodel of two-dimensional plane rotators: High-temperature expansions to order β20

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High-temperature series expansions of the spin-spin correlation function for the plane rotator (or XY) model on the square lattice are extended by three terms through order ${\mathrm{\ensuremath{\beta}}}^{20}$. Tables of the expansion coefficients are reported for the correlation function spherical moments of order l=0,1,2. The expansion coefficients through ${\mathrm{\ensuremath{\beta}}}^{15}$ for the vorticity are also tabulated. Our analysis of the series supports the Kosterlitz-Thouless predictions on the structure of the critical singularities and leads to fairly accurate estimates of the critical parameters.High-temperature series expansions of the spin-spin correlation function for the plane rotator (or XY) model on the square lattice are extended by three terms through order ${\mathrm{\ensuremath{\beta}}}^{20}$. Tables of the expansion coefficients are reported for the correlation function spherical moments of order l=0,1,2. The expansion coefficients through ${\mathrm{\ensuremath{\beta}}}^{15}$ for the vorticity are also tabulated. Our analysis of the series supports the Kosterlitz-Thouless predictions on the structure of the critical singularities and leads to fairly accurate estimates of the critical parameters.

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The bivariate high-temperature expansion of the spin-spin correlation function of the three-dimensional classical

XY

(planar rotator) model, with spatially anisotropic nearest-neighbor couplings, is extended from the tenth through the 21st order. The computation is carried out for the simple cubic lattice, in the absence of magnetic field, in the case in which the coupling strength along the

z

axis of the lattice is different from those along the

x

and the

y

axes. It is then possible to determine accurately the critical temperature as function of the parameter

R

which characterizes the coupling anisotropy and to check numerically the universality, with respect to

R

, of the critical exponents of the three-dimensional anisotropic system. The analysis of our data also shows that the main predictions of the generalized scaling theory for the crossover from the three-dimensional to the two-dimensional critical behavior are compatible with the series extrapolations.