{
  "id": "1206.2952",
  "version": "v1",
  "published": "2012-06-13T22:04:26.000Z",
  "updated": "2012-06-13T22:04:26.000Z",
  "title": "Slow dynamics for the dilute Ising model in the phase coexistence region",
  "authors": [
    "Marc Wouts"
  ],
  "comment": "44 pages, 6 figures",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech"
  ],
  "abstract": "In this paper we consider the Glauber dynamics for a disordered ferromagnetic Ising model, in the region of phase coexistence. It was conjectured several decades ago that the spin autocorrelation decays as a negative power of time [Huse and Fisher, Phys. Rev. B, 1987]. We confirm this behavior by establishing a corresponding lower bound in any dimensions $d \\geqslant 2$, together with an upper bound when $d=2$. Our approach is deeply connected to the Wulff construction for the dilute Ising model. We consider initial phase profiles with a reduced surface tension on their boundary and prove that, under mild conditions, those profiles are separated from the (equilibrium) pure plus phase by an energy barrier.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-13T22:04:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B44",
      "82C20",
      "60K35"
    ],
    "keywords": [
      "dilute ising model",
      "phase coexistence region",
      "slow dynamics",
      "initial phase profiles",
      "spin autocorrelation decays"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00220-012-1590-0",
      "journal": "Communications in Mathematical Physics",
      "year": 2013,
      "month": "Jan",
      "volume": 317,
      "number": 2,
      "pages": 381
    },
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013CMaPh.317..381W"
    }
  }
}