Theory of phase-ordering kinetics

TLDR

The theory of phase‑ordering dynamics, i.e., growth of order through domain coarsening after a quench into a broken‑symmetry phase, is reviewed with emphasis on recent developments and is relevant for experimentally studied systems such as nematic liquid crystals. The study focuses on the long‑time scaling regime after a quench, aiming to determine the growth laws for characteristic length scales and the form of the associated scaling functions. The analysis examines systems with vector and tensor order parameters, using topological defect dynamics—domain walls, vortices, strings, and monopoles—as a unifying framework for coarsening.

Abstract

Abstract The theory of phase-ordering dynamics, that is 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, for example 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 and monopoles) provides a unifying framework for discussing coarsening in these different systems.