Phase Ordering Kinetics with External Fields and Biased Initial Conditions

TL;DR

This paper studies the late-time phase-ordering kinetics of the O(n) model under external fields or biased initial conditions, using a gaussian closure approach to analyze order parameters, correlations, and defect densities.

Contribution

It introduces an approximate gaussian closure method to analyze phase-ordering kinetics with symmetry-breaking initial conditions or external fields.

Findings

Results agree qualitatively with experiments on nematic films.

Theoretical predictions match numerical simulations of the 2D XY model.

Provides insights into defect dynamics under symmetry-breaking conditions.

Abstract

The late-time phase-ordering kinetics of the O(n) model for a non-conserved order parameter are considered for the case where the O(n) symmetry is broken by the initial conditions or by an external field. An approximate theoretical approach, based on a `gaussian closure' scheme, is developed, and results are obtained for the time-dependence of the mean order parameter, the pair correlation function, the autocorrelation function, and the density of topological defects [e.g. domain walls ($n=1$), or vortices ($n=2$)]. The results are in qualitative agreement with experiments on nematic films and related numerical simulations on the two-dimensional XY model with biased initial conditions.