{
  "id": "1010.0560",
  "version": "v2",
  "published": "2010-10-04T12:23:53.000Z",
  "updated": "2010-11-19T09:19:24.000Z",
  "title": "Dynamic crossover in the persistence probability of manifolds at criticality",
  "authors": [
    "Andrea Gambassi",
    "Raja Paul",
    "Gregory Schehr"
  ],
  "comment": "23 pages, 6 figures; minor changes, added one figure, (old) fig.4 replaced by the correct fig.5",
  "journal": "J. Stat. Mech. (2010) P12029",
  "doi": "10.1088/1742-5468/2010/12/P12029",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We investigate the persistence properties of critical d-dimensional systems relaxing from an initial state with non-vanishing order parameter (e.g., the magnetization in the Ising model), focusing on the dynamics of the global order parameter of a d'-dimensional manifold. The persistence probability P(t) shows three distinct long-time decays depending on the value of the parameter \\zeta = (D-2+\\eta)/z which also controls the relaxation of the persistence probability in the case of a disordered initial state (vanishing order parameter) as a function of the codimension D = d-d' and of the critical exponents z and \\eta. We find that the asymptotic behavior of P(t) is exponential for \\zeta > 1, stretched exponential for 0 <= \\zeta <= 1, and algebraic for \\zeta < 0. Whereas the exponential and stretched exponential relaxations are not affected by the initial value of the order parameter, we predict and observe a crossover between two different power-law decays when the algebraic relaxation occurs, as in the case d'=d of the global order parameter. We confirm via Monte Carlo simulations our analytical predictions by studying the magnetization of a line and of a plane of the two- and three-dimensional Ising model, respectively, with Glauber dynamics. The measured exponents of the ultimate algebraic decays are in a rather good agreement with our analytical predictions for the Ising universality class. In spite of this agreement, the expected scaling behavior of the persistence probability as a function of time and of the initial value of the order parameter remains problematic. In this context, the non-equilibrium dynamics of the O(n) model in the limit n->\\infty and its subtle connection with the spherical model is also discussed in detail.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-11-19T09:19:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "persistence probability",
      "dynamic crossover",
      "criticality",
      "global order parameter",
      "distinct long-time decays depending"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Mechanics: Theory and Experiment",
      "year": 2010,
      "month": "Dec",
      "volume": 2010,
      "number": 12,
      "pages": 12029
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JSMTE..12..029G"
    }
  }
}