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

TL;DR

This paper advances the theoretical understanding of phase ordering in the O(2) model by incorporating post-gaussian corrections, leading to more accurate predictions of correlation functions and defect densities in two and three dimensions.

Contribution

It introduces a post-gaussian approximation for the O(2) model, improving upon the gaussian closure approximation and providing refined analytical expressions for key physical quantities.

Findings

Post-gaussian corrections improve agreement with simulations.

Derived formulae for defect density and correlations.

Calculated the decay exponent of order-parameter auto-correlations.

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 non-trivial 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 formulae for the defect density and the defect-defect correlation function $\tilde{g}(x)$ are derived. As in the previous gaussian theory, the addition of fluctuations allows one to eliminate the unphysical divergence in $\tilde{g}(x)$ at short scaled-distances. The non-trivial exponent $\lambda$, governing the decay of order-parameter auto-correlations, is computed in this approximation both with and without fluctuations.