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Slow Logarithmic Decay of Magnetization in the Zero Temperature Dynamics of an Ising Spin Chain: Analogy to Granular Compaction | | Satya N. Majumdar
; David S. Dean
; Peter Grassberger
; | | Date: |
28 Apr 2000 | | Journal: | Phys. Rev. Lett., 86 (2001) 2301. | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | 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, $m(t)=-1 +{
m const.}/{log (t)}$. 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. | | Source: | arXiv, cond-mat/0004486 | | Services: | Forum | Review | PDF | Favorites | |
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