Critical dynamics in the two-dimensional classical XY model: A spin-dynamics study

Using spin-dynamics techniques we have performed large-scale computer simulations of the dynamic behavior of the classical three component XY model (i.e., the anisotropic limit of an easy-plane Heisenberg ferromagnet), on square lattices of size up to ${192}^2$, for several temperatures below, at, and above ${\mathit{T}}_{\mathrm{KT}}$. The temporal evolution of spin configurations was determined numerically from coupled equations of motion for individual spins by a fourth-order predictor-corrector method, with initial spin configurations generated by a hybrid Monte Carlo algorithm. The neutron-scattering function S(q,ω) was calculated from the resultant space-time displaced spin-spin correlation function. Pronounced spin-wave peaks were found both in the in-plane and the out-of-plane scattering function over a wide range of temperatures. The in-plane scattering function ${\mathit{S}}^{\mathit{xx}}$ also has a large number of clear but weak additional peaks, which we interpret to come from two-spin-wave scattering. In addition, we observed a small central peak in ${\mathit{S}}^{\mathit{xx}}$, even at temperatures well below the phase transition. We used dynamic finite-size scaling theory to extract the dynamic critical exponent z. We find z=1.00(4) for all T≤${\mathit{T}}_{\mathrm{KT}}$, in excellent agreement with theoretical predictions, although the shape of S(q,ω) is not well described by current theory. © 1996 The American Physical Society.