Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2000-04-28
Phys. Rev. Lett., 86 (2001) 2301.
Physics
Condensed Matter
Statistical Mechanics
4 pages Revtex, 3 eps figures, supersedes cond-mat/0002217
Scientific paper
10.1103/PhysRevLett.86.2301
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.
Dean David S.
Grassberger Peter
Majumdar Satya N.
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