Coarsening in a Driven Ising Chain with Conserved Dynamics

TL;DR

This paper investigates the coarsening dynamics of a driven Ising chain with conserved spin-exchange, revealing two distinct length scales and non-scaling behavior in domain size distribution at low temperatures.

Contribution

It introduces a detailed analysis of driven Ising chain coarsening, highlighting the emergence of two independent length scales and their impact on domain distribution scaling.

Findings

Two independent length scales: L(t)~t^{1/2} and l(t)~ t^{1/4}.

Domain size distribution does not obey scaling laws.

Short domain density decays as t^{-5/4} instead of t^{-3/2}.

Abstract

We study the low-temperature coarsening of an Ising chain subject to spin-exchange dynamics and a small driving force. This dynamical system reduces to a domain diffusion process, in which entire domains undergo nearest-neighbor hopping, except for the shortest domains -- dimers -- which undergo long-range hopping. This system is characterized by two independent length scales: the average domain length L(t)~t^{1/2} and the average dimer hopping distance l(t)~ t^{1/4}. As a consequence of these two scales, the density C_k(t) of domains of length k does not obey scaling. This breakdown of scaling also leads to the density of short domains decaying as t^{-5/4}, instead of the t^{-3/2} decay that would arise from pure domain diffusion.