Phase ordering of the O(2) model in the post-Gaussian approximation

Abstract

The Gaussian closure approximation previously used to study the growth kinetics of the non-conserved O(n) model is shown to be the zeroth-order approximation in a well-defined sequence of approximations composing a more elaborate theory. This paper studies the effects of including the next nontrivial correction in this sequence for the case n=2. The scaling forms for the order-parameter and order-parameter squared correlation functions are determined for the physically interesting cases of the O(2) model in two and three spatial dimensions. The post-Gaussian versions of these quantities show improved agreement with simulations. Post-Gaussian formulas for the defect density and the defect-defect correlation function g-tilde(x) are derived. As in the previous Gaussian theory, the addition of fluctuations allows one to eliminate the unphysical divergence in g-tilde(x) at short scaled distances. The nontrivial exponent \ensuremath{\lambda}, governing the decay of order-parameter autocorrelations, is computed in this approximation both with and without fluctuations.