Coarsening in a driven Ising chain with conserved dynamics

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 exhibits anomalous ordering dynamics due to the existence of two characteristic length scales: the average domain length $L\left(t\right)\mathrm{}\sim t^{1/2}$ and the average dimer hopping distance $\mathcal{l}\mathrm{}\left(t\right)\mathrm{}\sim \sqrt{L\left(t\right)\mathrm{}}\sim t^{1/4}.$ As a consequence of these two scales, the density of short domains decays as $t^{-5/4},$ instead of the $t^{-3/2}$ decay that would arise from pure domain diffusion.