A quantitative study of the Kosterlitz-Thouless phase transition in a system of two-dimensional plane rotators (XY model) by high temperature expansions through 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 β²⁰. Tables of the expansion coefficients are reported for the correlation function spherical moments of order l=0,1,2. The expansion coefficients through β¹⁵ 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.