Phase Transition in the2D XYModel

We present detailed results for the susceptibility $\chi$, correlation length $\xi$, and specific heat $c_{\nu }$ for the $\mathrm{XY}$ model. The best fit to $\chi$ and $\xi$ data is obtained by use of the Kosterlitz-Thouless scaling form with $\nu =0.500\mathrm{}\left(1\right)\mathrm{}$, but $\eta$ shows considerable deviation from ¼ down to $T=1.03\mathrm{}$. The critical temperature is estimated to be $T_c=0.898\mathrm{}\left(2\right)\mathrm{}$. The simulations are done on ${64}^2$, ${128}^2$, ${256}^2$, and ${512}^2$ lattices with use of an overrelaxed algorithm which decorrelates as $\tau \approx 0.15{\xi }^{1.2}$. Similar reduction in critical slowing down is anticipated for all continuous-spin models.