Critical behavior of the two-dimensional XY model.

摘要: We present detailed Monte Carlo results for the susceptibility \ensuremath{\chi}, correlation length \ensuremath{\xi}, and specific heat ${\mathit{C}}_{\mathit{v}}$ XY model. The simulations are done on ${64}^{2}$, ${128}^{2}$, ${256}^{2}$, ${512}^{2}$ lattices over temperature range 0.98\ensuremath{\le}T\ensuremath{\le}1.43 corresponding to 270. Fits \ensuremath{\chi} \ensuremath{\xi} data favor a Kosterlitz-Thouless (KT) singularity second-order transition; however, unconstrained four-parameter KT fits do not confirm predicted values \ensuremath{\nu}=0.5 \ensuremath{\eta}=0.25. Our best estimate, ${\mathit{T}}_{\mathit{c}}$=0.894(5), is obtained using with \ensuremath{\nu} fixed at 0.5. exponent \ensuremath{\eta} calculated as function of in spin-wave phase renormalization-group finite-size-scaling methods. Both methods give consistent we find \ensuremath{\eta}\ensuremath{\approxeq}0.235 T=0.894. also behavior vortex density across transition exhibit how dilute-gas approximation breaks down.