Growth Laws for Phase Ordering

TL;DR

This paper derives growth laws for the characteristic length scale in phase ordering kinetics across various models, providing a unified approach to understanding domain growth in systems with different interactions and conservation laws.

Contribution

It introduces a consistent method to determine the growth law by comparing energy change rates and applies it to derive laws for O(n) models and similar systems.

Findings

Derived growth laws for scalar and vector fields.

Unified approach applicable to systems with short- or long-range interactions.

Results relevant for systems with defect structures.

Abstract

We determine the characteristic length scale, $L(t)$, in phase ordering kinetics for both scalar and vector fields, with either short- or long-range interactions, and with or without conservation laws. We obtain $L(t)$ consistently by comparing the global rate of energy change to the energy dissipation from the local evolution of the order parameter. We derive growth laws for O(n) models, and our results can be applied to other systems with similar defect structures.