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arXiv:cond-mat/9902326 · Physical review. B, Condensed matter

High-temperature study of the Kosterlitz-Thouless phase transition in theXYmodel on the triangular lattice

P. Butera, M. Comi

Published Aug 1, 1994• 35 citations
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Abstract

High-temperature series expansions of the spin-spin correlation function for the XY (or plane rotator) model on the triangular lattice are extended by two terms up to order ${\mathrm{\ensuremath{\beta}}}^{14}$. Tables of the expansion coefficients are reported for the correlaton function spherical moments of order l=0 and 2. 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.

DOI
10.1103/physrevb.50.3052

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High-temperature series expansions of the spin-spin correlation function for the XY (or plane rotator) model on the triangular lattice are extended by two terms up to order \ensuremathβ14{\mathrm{\ensuremath{\beta}}}^{14}\ensuremathβ14. Tables of the expansion coefficients are reported for the correlaton function spherical moments of order l=0 and 2. 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.
High-temperature series are extended through ${\ensuremath{\beta}}^{17}$ for the susceptibility and for the first and second moments of the correlation functions, in the case of the classical two-dimensional O(2) Heisenberg model (also called the XY model). For the ``true mass gap'' the high-temperature expansion is computed through ${\ensuremath{\beta}}^{12}$. The calculations are performed by a new computer program which solves iteratively the Schwinger-Dyson equations of the model. Ratio-extrapolation, Euler-transform and Pad\'e techniques are used to analyze the series and to discriminate between the recently reproposed conventional power-law form of the critical singularity and the form predicted by Kosterlitz and Thouless. The critical parameters are determined for the Kosterlitz-Thouless form, which is clearly favored by our data.
In this paper we report analyses of high temperature series expansions for the spin [Formula: see text] XY model on the triangular and square lattices. Quantities for which series are analyzed include the fluctuation in the transverse magnetization, fourth order fluctuations in the same quantity, second and fourth moments of the transverse spin–spin correlations, specific heat, and entropy. The evidence favours a phase transition at a finite temperature with conventional power law critical singularities. Scaling seems to hold but hyperscaling seems to be violated. Estimates for critical exponents include γ = 2.50 ± 0.3. Δ = 2.38 ± 0.2, and ν = 143 ± 0.10. The specific heat exhibits no singular behaviour at Tc.