Effective mobility and diffusivity in coarsening processes

TL;DR

This paper models coarsening dynamics as a generalized random walk with drift and diffusion, applying it to the 1D Ising model, revealing different behaviors for Glauber and Kawasaki dynamics and suggesting similar effects in 2D.

Contribution

It introduces a generalized random walk framework to describe coarsening, analyzing the effects of drift and diffusion in different dynamics and dimensions.

Findings

Glauber dynamics shows speeding of coarsening in the pre-asymptotic regime.

Kawasaki dynamics exhibits a slowdown in coarsening.

The model suggests similar behaviors may occur in two-dimensional systems.

Abstract

We suggest that coarsening dynamics can be described in terms of a generalized random walk, with the dynamics of the growing length $L(t)$ controlled by a drift term, $\mu(L)$, and a diffusive one, ${\cal D}(L)$. We apply this interpretation to the one dimensional Ising model with a ferromagnetic coupling constant decreasing exponentially on the scale $R$. In the case of non conserved (Glauber) dynamics, both terms are present and their balance depend on the interplay between $L(t)$ and $R$. In the case of conserved (Kawasaki) dynamics, drift is negligible, but ${\cal D}(L)$ is strongly dependent on $L$. The main pre-asymptotic regime displays a speeding of coarsening for Glauber dynamics and a slowdown for Kawasaki dynamics. We reason that a similar behaviour can be found in two dimensions.