Domain Growth in a 1-D Driven Diffusive System

TL;DR

This paper analytically and numerically investigates the coarsening dynamics of a 1D driven Ising model with conserved magnetisation, revealing universal growth laws and domain-size distributions at low temperatures.

Contribution

It provides an analytical solution for domain growth and distribution in a driven 1D Ising model with small minority phase volume fraction, extending understanding of non-equilibrium coarsening.

Findings

Mean domain size grows as t^{1/2}

Domain-size distribution follows a specific exponential form

Persistence exponent for minority phase is 3/2 as 

Abstract

The low-temperature coarsening dynamics of a one-dimensional Ising model, with conserved magnetisation and subject to a small external driving force, is studied analytically in the limit where the volume fraction \mu of the minority phase is small, and numerically for general \mu. The mean domain size L(t) grows as t^{1/2} in all cases, and the domain-size distribution for domains of one sign is very well described by the form P_l(l) \propto (l/L^3)\exp[-\lambda(\mu)(l^2/L^2)], which is exact for small \mu (and possibly for all \mu). The persistence exponent for the minority phase has the value 3/2 for \mu \to 0.