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

摘要

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) over tilde(x) are derived. As in the previous Gaussian theory, the addition of fluctuations allows one to eliminate the unphysical divergence in (g) over tilde(x) at short scaled distances. The nontrivial exponent lambda, governing the decay of order-parameter autocorrelations, is computed in this approximation both with and without fluctuations.