A quantitative study of the Kosterlitz-Thouless phase transition in a system of two-dimensional plane rotators ( XY model ) by high temperature expansions through ${\beta }^{20}$

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