{
  "id": "cond-mat/0004486",
  "version": "v1",
  "published": "2000-04-28T12:35:05.000Z",
  "updated": "2000-04-28T12:35:05.000Z",
  "title": "Slow Logarithmic Decay of Magnetization in the Zero Temperature Dynamics of an Ising Spin Chain: Analogy to Granular Compaction",
  "authors": [
    "Satya N. Majumdar",
    "David S. Dean",
    "Peter Grassberger"
  ],
  "comment": "4 pages Revtex, 3 eps figures, supersedes cond-mat/0002217",
  "journal": "Phys. Rev. Lett., 86 (2001) 2301.",
  "doi": "10.1103/PhysRevLett.86.2301",
  "categories": [
    "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, $m(t)=-1 +{\\rm const.}/{\\log (t)}$. 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-04-28T12:35:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "zero temperature dynamics",
      "slow logarithmic decay",
      "ising spin chain",
      "granular compaction",
      "late times"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. Lett."
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}