Theory of Phase Ordering Kinetics

TL;DR

This paper reviews the theory of phase ordering kinetics, focusing on growth laws, scaling functions, and the role of topological defects in systems with complex order parameters like liquid crystals.

Contribution

It provides a comprehensive overview of recent developments in phase ordering dynamics, especially for systems with vector and tensor order parameters.

Findings

Analysis of growth laws and scaling functions in phase ordering

Discussion of topological defects in coarsening processes

Application to complex systems like nematic liquid crystals

Abstract

The theory of phase ordering dynamics -- the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken-symmetry phase -- is reviewed, with the emphasis on recent developments. Interest will focus on the scaling regime that develops at long times after the quench. How can one determine the growth laws that describe the time-dependence of characteristic length scales, and what can be said about the form of the associated scaling functions? Particular attention will be paid to systems described by more complicated order parameters than the simple scalars usually considered, e.g. vector and tensor fields. The latter are needed, for example, to describe phase ordering in nematic liquid crystals, on which there have been a number of recent experiments. The study of topological defects (domain walls, vortices, strings, monopoles) provides a unifying framework for discussing coarsening in these different systems.