Quantitative study of the Kosterlitz-Thouless phase transition in anXYmodel of two-dimensional plane rotators: High-temperature expansions to orderβ20

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 ${\mathrm{\beta }}^{20}$. Tables of the expansion coefficients are reported for the correlation function spherical moments of order l=0,1,2. The expansion coefficients through ${\mathrm{\beta }}^{15}$ 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.