Critical dynamics in the 2d classical XY-model: a spin dynamics study

TL;DR

This study uses large-scale spin-dynamics simulations to analyze the dynamic behavior of the 2D XY-model, revealing spin-wave phenomena and critical exponents consistent with theoretical predictions across various temperatures.

Contribution

First large-scale simulation of 2D XY-model dynamics capturing spin-wave peaks and critical behavior, with detailed analysis of scattering functions and critical exponents.

Findings

Pronounced spin-wave peaks observed in scattering functions.

Dynamic critical exponent z=1.00(4) consistent with theory.

Presence of a small central peak below T_KT.

Abstract

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 T_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,omega) 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 S^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 S^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 <= T_KT, in excellent agreement with theoretical predictions, although the shape of S(q,omega) is not well described by current theory.