Phase transition in the 2D XY model.

Abstract

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