Kinetics of phase ordering on curved surfaces

TL;DR

This paper investigates how phase ordering dynamics on curved surfaces differ from flat systems, revealing slower growth laws, breakdown of scaling, and metastable states due to surface curvature effects.

Contribution

It introduces a novel interface description and numerical approach to study phase ordering kinetics on curved surfaces, deriving geometrical dynamical equations and analyzing curvature effects.

Findings

Growth laws are slower than $t^{1/2}$ and logarithmic.

Dynamical scaling breaks down on curved surfaces.

Metastable states emerge due to the absence of a zero-temperature fixed point.

Abstract

An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intra-surface kinetics of phase ordering on corrugated surfaces. Geometrical dynamical equations are derived for the domain interfaces. The dynamics is shown to depend strongly on the local Gaussian curvature of the surface, and can be fundamentally different from that in flat systems: dynamical scaling breaks down despite the persistence of the dominant interfacial undulation mode; growth laws are slower than $t^{1/2}$ and even logarithmic; a new very-late-stage regime appears characterized by extremely slow interface motion; finally, the zero-temperature fixed point no longer exists, leading to metastable states. Criteria for the existence of the latter are derived and discussed in the context of more complex systems.