Slow Logarithmic Decay of Magnetization in the Zero Temperature Dynamics of an Ising Spin Chain: Analogy to Granular Compaction

Abstract

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, $m(t)=-1+const./\log (t)$. 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.

4 pages Revtex, 3 eps figures, supersedes cond-mat/0002217

References in corpus (2)

• Glassy timescale divergence and anomalous coarsening in a kinetically constrained spin chain
• Critical behaviour of annihilating random walk of two species with exclusion in one dimension

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