We calculate the high-temperature series of the magnetic susceptibility and the second and fourth moments of the correlation function for the XY model on the square lattice to order $\beta^{ 33}$ by applying the improved algorithm of the finite lattice method. The long series allow us to estimate the inverse critical temperature as $\beta_c=1.1200(1)$, which is consistent with the most precise value given previously by the Monte Carlo simulation. The critical exponent for the multiplicative logarithmic correction is evaluated to be $\theta=0.054(10)$, which is consistent with the renormalization group prediction of $\theta={ 1/16}$.
Categories: cond-mat.stat-mech