{
  "id": "1212.2956",
  "version": "v2",
  "published": "2012-12-12T20:55:27.000Z",
  "updated": "2013-02-07T13:19:19.000Z",
  "title": "Time scale separation in the low temperature East model: Rigorous results",
  "authors": [
    "Paul Chleboun",
    "Alessandra Faggionato",
    "Fabio Martinelli"
  ],
  "comment": "6 pages, 0 figures; clarified q dependence of bounds, results unchanged",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the non-equilibrium dynamics of the East model, a linear chain of 0-1 spins evolving under a simple Glauber dynamics in the presence of a kinetic constraint which forbids flips of those spins whose left neighbour is 1. We focus on the glassy effects caused by the kinetic constraint as $q\\downarrow 0$, where $q$ is the equilibrium density of the 0's. Specifically we analyse time scale separation and dynamic heterogeneity, i.e. non-trivial spatio-temporal fluctuations of the local relaxation to equilibrium, one of the central aspects of glassy dynamics. For any mesoscopic length scale $L=O(q^{-\\gamma})$, $\\gamma<1$, we show that the characteristic time scale associated to two length scales $d/q^\\gamma$ and $d'/q^\\gamma$ are indeed separated by a factor $q^{-a}$, $a=a(\\gamma)>0$, provided that $d'/d$ is large enough independently of $q$. In particular, the evolution of mesoscopic domains, i.e. maximal blocks of the form $111..10$, occurs on a time scale which depends sharply on the size of the domain, a clear signature of dynamic heterogeneity. Finally we show that no form of time scale separation can occur for $\\gamma=1$, i.e. at the equilibrium scale $L=1/q$, contrary to what was previously assumed in the physical literature based on numerical simulations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-02-07T13:19:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "low temperature east model",
      "rigorous results",
      "length scale",
      "kinetic constraint",
      "analyse time scale separation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1742-5468/2013/04/L04001",
      "journal": "Journal of Statistical Mechanics: Theory and Experiment",
      "year": 2013,
      "month": "Apr",
      "volume": 2013,
      "number": 4
    },
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JSMTE..04..000C"
    }
  }
}