Fluctuations and defect-defect correlations in the ordering kinetics of the O(2) model

TL;DR

This paper revisits the phase ordering kinetics of the O(2) model, incorporating fluctuations and analyticity considerations, leading to refined defect correlation functions and modified autocorrelation exponents.

Contribution

It introduces a refined gaussian auxiliary field theory for the O(2) model that accounts for fluctuations and ensures analyticity, removing divergences in defect correlations.

Findings

Divergence at the origin in defect-defect correlation function is removed.

Modifications to the order-parameter autocorrelation exponent λ are computed.

The theory now includes fluctuation effects and is organized for analyticity in short-scaled distance expansion.

Abstract

The theory of phase ordering kinetics for the O(2) model using the gaussian auxiliary field approach is reexamined from two points of view. The effects of fluctuations about the ordering field are included and we organize the theory such that the auxiliary field correlation function is analytic in the short-scaled distance (x) expansion. These two points are connected and we find in the refined theory that the divergence at the origin in the defect-defect correlation function $\tilde{g}(x)$ obtained in the original theory is removed. Modifications to the order-parameter autocorrelation exponent $\lambda$ are computed.