Contrasts between coarsening and relaxational dynamics of surfaces

TL;DR

This paper compares the static and dynamic behaviors of domain walls in crystalline surfaces, revealing different scaling exponents for relaxation and coarsening processes through analytical and numerical methods.

Contribution

It provides a novel analysis of the contrasting exponents governing relaxation and coarsening in surface domain walls, differing from classical Ising-like models.

Findings

Dynamic exponent z=2 for relaxation

Coarsening exponent n=1/4 for steady-state formation

Distinct scaling behaviors for relaxation and coarsening processes

Abstract

We discuss static and dynamic fluctuations of domain walls separating areas of constant but different slopes in steady-state configurations of crystalline surfaces both by an analytic treatment of the appropriate Langevin equation and by numerical simulations. In contrast to other situations that describe the dynamics in Ising-like systems such as models A and B, we find that the dynamic exponent z=2 that governs the domain wall relaxation function is not equal to the inverse of the exponent n=1/4 that describes the coarsening process that leads to the steady state.