{
  "id": "1005.4491",
  "version": "v1",
  "published": "2010-05-25T07:09:37.000Z",
  "updated": "2010-05-25T07:09:37.000Z",
  "title": "Universality of the glassy transitions in the two-dimensional +- J Ising model",
  "authors": [
    "Francesco Parisen Toldin",
    "Andrea Pelissetto",
    "Ettore Vicari"
  ],
  "comment": "9 pages, 17 figs",
  "journal": "Phys. Rev. E 82 (2010) 021106",
  "doi": "10.1103/PhysRevE.82.021106",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "We investigate the zero-temperature glassy transitions in the square-lattice +- J Ising model, with bond distribution $P(J_{xy}) = p \\delta(J_{xy} - J) + (1-p) \\delta(J_{xy} + J)$; p=1 and p=1/2 correspond to the pure Ising model and to the Ising spin glass with symmetric bimodal distribution, respectively. We present finite-temperature Monte Carlo simulations at p=4/5, which is close to the low-temperature paramagnetic-ferromagnetic transition line located at p=0.89, and at p=1/2. Their comparison provides a strong evidence that the glassy critical behavior that occurs for $1-p_0<p<p_0$, $p_0=0.897$, is universal, i.e., independent of p. Moreover, we show that glassy and magnetic modes are not coupled at the multicritical zero-temperature point where the paramagnetic-ferromagnetic transition line and the T=0 glassy transition line meet. On the theoretical side we discuss the validity of finite-size scaling in glassy systems with a zero-temperature transition and a discrete Hamiltonian spectrum. Because of a freezing phenomenon which occurs in a finite volume at sufficiently low temperatures, the standard finite-size scaling limit in terms of $TL^{1/\\nu}$ does not exist: the renormalization-group invariant quantity $\\xi/L$ should be used instead as basic variable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-25T07:09:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "64.60.F-",
      "75.10.Nr",
      "75.50.Lk",
      "75.40.Mg"
    ],
    "keywords": [
      "ising model",
      "finite-temperature monte carlo simulations",
      "universality",
      "two-dimensional",
      "glassy transition line meet"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2010,
      "month": "Aug",
      "volume": 82,
      "number": 2,
      "pages": "021106"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010PhRvE..82b1106P"
    }
  }
}