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We present detailed analytical studies on the zero temperature coarseningdynamics in an Ising spin chain in presence of a dynamically induced field thatfavors locally the `-' phase compared to the `+' phase. We show that thepresence of such a local kinetic bias drives the system into a late time statewith average magnetization m=-1. However the magnetization relaxes into thisfinal value extremely slowly in an inverse logarithmic fashion. We further mapthis spin model exactly onto a simple lattice model of granular compaction thatincludes the minimal microscopic moves needed for compaction. This toy modelthen predicts analytically an inverse logarithmic law for the growth of densityof granular particles, as seen in recent experiments and thereby provides a newmechanism for the inverse logarithmic relaxation. Our analysis utilizes anindependent interval approximation for the particle and the hole clusters andis argued to be exact at late times (supported also by numerical simulations).Comment: 9 pages RevTeX, 1 figures (.eps

Slow relaxation in a constrained Ising spin chain: Toy model for granular compaction