Gaussian Approach for Phase Ordering in Nonconserved Scalar Systems with Long-Range Interactions

TL;DR

This paper applies the gaussian auxiliary field method to study phase ordering in non-conserved scalar systems with long-range interactions, revealing limitations of the approach in capturing growth laws.

Contribution

It tests the gaussian auxiliary field method on long-range interacting systems and highlights its difficulties and inconsistencies in predicting growth behavior.

Findings

Obtains Porod regime and power-law decay in correlation functions.

Identifies inconsistencies with expected growth laws.

Shows failure of the gaussian assumption for this system.

Abstract

We have applied the gaussian auxiliary field method introduced by Mazenko to the ordering dynamics of a non-conserved scalar system with attractive long-range interactions. This study provides a test-bed for the approach and shows some of the difficulties encountered in constructing a closed theory for the pair correlation function. The equation obtained for the equal-time two-point correlation function is studied in the limiting cases of small and large values of the scaling variable. A Porod regime at short distance and an asymptotic power-law decay at large distance are obtained. The theory, is not, however, consistent with the expected growth-law, and attempts to retrieve the correct growth lead to inconsistencies. These results indicate a failure of the gaussian assumption (at least in the form in which we use it) for this system.