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

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 $\theta =1\mathrm{/}16$.