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We calculate the high-temperature series of the magnetic susceptibility andthe second and fourth moments of the correlation function for the XY model onthe square lattice to order $\beta^{33}$ by applying the improved algorithm ofthe finite lattice method. The long series allow us to estimate the inversecritical temperature as $\beta_c=1.1200(1)$, which is consistent with the mostprecise value given previously by the Monte Carlo simulation. The criticalexponent for the multiplicative logarithmic correction is evaluated to be$\theta=0.054(10)$, which is consistent with the renormalization groupprediction of $\theta={1/16}$.

High-temperature expansion of the magnetic susceptibility and higher moments of the correlation function for the two-dimensional XY model