Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-lat/9209011 · Physical review. B, Condensed matter

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

P. Butera, M. Comi

Published May 1, 1993• 46 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.47.11969

Related papers

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

P. Butera, M. Comi

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.

arXiv:cond-mat/9902326•Physical review. B, Condensed matter•Aug 1, 1994•35 citations

Critical exponents of the three-dimensional classical plane-rotator model on the sc lattice from a high-temperature-series analysis

P. Butera, M. Comi, Anthony John Guttmann

High-temperature-series expansions of the spin-spin correlation function for the plane-rotator (or XY) model on the sc lattice are extended by three terms through order ${\mathrm{\ensuremath{\beta}}}^{17}$. Tables of the expansion coefficients are reported for the correlation function spherical moments of order l=0,1,2. Our analysis of the series leads to fairly accurate estimates of the critical parameters.

arXiv:hep-lat/9305002•Physical review. B, Condensed matter•Nov 1, 1993•15 citations

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

P. Butera, M. Pernici

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.

arXiv:0710.0338•Physical Review B•Sep 26, 2007•9 citations

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

P. Butera, M. Pernici

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.

arXiv:0806.1496•Jun 9, 2008•0 citations

Critical behavior of the two-dimensionalXYmodel: An analysis of extended high-temperature series

P. Butera, M. Comi, G. Marchesini

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.

Physical review. B, Condensed matter•Jul 1, 1989•21 citations

Perturbative renormalization group, exact results, and high-temperature series to order 21 for theN-vector spin models on the square lattice

P. Butera, M. Comi

High-temperature expansions for the susceptibility and the second correlation moment of the classical N-vector model [also known as the O(N) symmetric Heisenberg classical spin model] on the square lattice are extended from order ${\mathrm{\ensuremath{\beta}}}^{14}$ to ${\mathrm{\ensuremath{\beta}}}^{21}$ for arbitrary N. For the second field derivative of the susceptibility the series expansion is extended from order ${\mathrm{\ensuremath{\beta}}}^{14}$ to ${\mathrm{\ensuremath{\beta}}}^{17}$. For -2\ensuremath{\le}N2, a numerical analysis of the series is performed in order to compare the critical exponents \ensuremath{\gamma}(N), \ensuremath{\nu}(N), and \ensuremath{\Delta}(N) to exact (though nonrigorous) formulas and to compute the ``dimensionless four point coupling constant'' g${\mathrm{^}}_{\mathit{r}}$(N). For N>2, we present a study of the analyticity properties of \ensuremath{\chi}, \ensuremath{\xi}, etc. in the complex \ensuremath{\beta} plane and describe a method to estimate the parameters which characterize their low-temperature behaviors. We compare our series estimates to the predictions of the perturbative renormalization group theory, to exact (but nonrigorous or conjectured) formulas and to the results of the 1/N expansion, always finding a good agreement. \textcopyright{} 1996 The American Physical Society.

arXiv:hep-lat/9710092•Physical review. B, Condensed matter•Dec 1, 1996•50 citations
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 \ensuremathβ20{\mathrm{\ensuremath{\beta}}}^{20}\ensuremathβ20. Tables of the expansion coefficients are reported for the correlation function spherical moments of order l=0,1,2. The expansion coefficients through \ensuremathβ15{\mathrm{\ensuremath{\beta}}}^{15}\ensuremathβ15 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 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.
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.
High-temperature expansions for the susceptibility and the second correlation moment of the classical N-vector model [also known as the O(N) symmetric Heisenberg classical spin model] on the square lattice are extended from order ${\mathrm{\ensuremath{\beta}}}^{14}$ to ${\mathrm{\ensuremath{\beta}}}^{21}$ for arbitrary N. For the second field derivative of the susceptibility the series expansion is extended from order ${\mathrm{\ensuremath{\beta}}}^{14}$ to ${\mathrm{\ensuremath{\beta}}}^{17}$. For -2\ensuremath{\le}N2, a numerical analysis of the series is performed in order to compare the critical exponents \ensuremath{\gamma}(N), \ensuremath{\nu}(N), and \ensuremath{\Delta}(N) to exact (though nonrigorous) formulas and to compute the ``dimensionless four point coupling constant'' g${\mathrm{^}}_{\mathit{r}}$(N). For N>2, we present a study of the analyticity properties of \ensuremath{\chi}, \ensuremath{\xi}, etc. in the complex \ensuremath{\beta} plane and describe a method to estimate the parameters which characterize their low-temperature behaviors. We compare our series estimates to the predictions of the perturbative renormalization group theory, to exact (but nonrigorous or conjectured) formulas and to the results of the 1/N expansion, always finding a good agreement. \textcopyright{} 1996 The American Physical Society.