We study the zero temperature coarsening dynamics in an Ising chain in presence of a dynamically induced field that favors locally the `-' phase compared to the `+' phase. At late times, while the `+' domains still coarsen as $t^{ 1/2}$, the `-' domains coarsen slightly faster as $t^{ 1/2}\log (t)$. As a result, at late times, the magnetization decays slowly as, $m(t)=-1 +{ \rm const.}/{ \log (t)}$. We establish this behavior both analytically within an independent interval approximation (IIA) and numerically. In the zero volume fraction limit of the `+' phase, we argue that the IIA becomes asymptotically exact. Our model can be alternately viewed as a simple Ising model for granular compaction. At late times in our model, the system decays into a fully compact state (where all spins are `-') in a slow logarithmic manner $\sim 1/{ \log (t)}$, a fact that has been observed in recent experiments on granular systems.
Categories: cond-mat.stat-mech