Kinetics of phase ordering in the O(n) model with a conserved order parameter

Abstract

We study the phase-ordering dynamics of the O(n) model with a conserved order parameter for systems with topological defects. We present results from both cell dynamical simulations and predictions of a Gaussian auxiliary field (GAF) approximation for the XY (n=2) model in two and three dimensions, and the Heisenberg (n=3) model in three dimensions. We describe the results for the structure factor S(q) and growth law L(t) from simulations. The growth laws obtained are consistent with theoretical predictions based on energy-scaling arguments. The structure factor shows good dynamical scaling using a length extracted from its first moment. The simulations are compared with the theoretical predictions of the GAF for the scaling functions. Our results show that the GAF gives a good qualitative description of most features of the structure factor. However, it overestimates the amplitude of the Porod tail in the large-q limit. Moreover, for small q, the structure factor exhibits a q²-behaviour instead of the expected (generalized) Yeung result of q⁴.