On the Nature of the Gaussian Approximations in Phase Ordering Kinetics s

TL;DR

This paper analyzes the Gaussian auxiliary field approximation in phase ordering kinetics, aiming to contextualize it within a systematic theory, especially for vector order parameter systems using a $1/N$-expansion.

Contribution

It provides a systematic development of the Gaussian approximation for vector order parameters via a $1/N$-expansion, contrasting with the uncontrolled scalar case.

Findings

Systematic framework for vector order parameters

Analysis of Gaussian approximation limitations

Potential for controlled approximation methods

Abstract

The structure of the gaussian auxiliary field approximation in the theory of phase ordering kinetics is analysed with the aim of placing the method within the context of a systematic theory. While we are unable to do this for systems with a scalar order parameter, where the approximation remains uncontrolled, a systematic development about the gaussian approximation can be outlined for systems with a vector order parameter in terms of a suitably defined $1/N$-expansion.