{
  "id": "math/0203234",
  "version": "v1",
  "published": "2002-03-22T15:52:27.000Z",
  "updated": "2002-03-22T15:52:27.000Z",
  "title": "Convergence in Energy-Lowering (Disordered) Stochastic Spin Systems",
  "authors": [
    "Emilio De Santis",
    "Charles M. Newman"
  ],
  "comment": "11 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider stochastic processes, S^t \\equiv (S_x^t : x \\in Z^d), with each S_x^t taking values in some fixed finite set, in which spin flips (i.e., changes of S_x^t) do not raise the energy. We extend earlier results of Nanda-Newman-Stein that each site x has almost surely only finitely many flips that strictly lower the energy and thus that in models without zero-energy flips there is convergence to an absorbing state. In particular, the assumption of finite mean energy density can be eliminated by constructing a percolation-theoretic Lyapunov function density as a substitute for the mean energy density. Our results apply to random energy functions with a translation-invariant distribution and to quite general (not necessarily Markovian) dynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-03-22T15:52:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K37",
      "82C44"
    ],
    "keywords": [
      "stochastic spin systems",
      "convergence",
      "finite mean energy density",
      "percolation-theoretic lyapunov function density",
      "random energy functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......3234D"
    }
  }
}