Coarsening in the Presence of Kinetic Disorders: Analogy to Granular Compaction

We study the zero temperature dynamics in an Ising chain in the presence of a dynamically induced field that favors locally the “ $-$” phase compared to the “ $+$” phase. At late times, while the “ $+$” domains coarsen as $t^{1/2}$, the “ $-$” domains coarsen as $t^{1/2}\log \left(t\right)$. Hence, at late times, the magnetization decays slowly as $m\left(t\right)=-1+\mathrm{const}/\log \left(t\right)$. We establish this behavior both analytically within an independent interval approximation and numerically. Our model can be viewed as a simple model for granular compaction, where the system decays into a fully compact state (with all spins “ $-$”) in a slow logarithmic manner as seen in recent experiments on granular systems.