{
  "id": "1412.2448",
  "version": "v1",
  "published": "2014-12-08T05:02:23.000Z",
  "updated": "2014-12-08T05:02:23.000Z",
  "title": "Critical Point Scaling of Ising Spin Glasses in a Magnetic Field",
  "authors": [
    "Joonhyun Yeo",
    "M. A. Moore"
  ],
  "comment": "9 pages, 12 figures",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "Critical point scaling in a field $H$ applies for the limits $t\\to 0$, (where $t=T/T_c-1$) and $H\\to 0$ but with the ratio $R=t/H^{2/\\Delta}$ finite. $\\Delta$ is a critical exponent of the zero-field transition. We study the replicon correlation length $\\xi$ and from it the crossover scaling function $f(R)$ defined via $1/(\\xi H^{4/(d+2-\\eta)}) \\sim f(R)$. We have calculated analytically $f(R)$ for the mean-field limit of the Sherrington-Kirkpatrick model. In dimension d=3 we have determined the exponents and the critical scaling function $f(R)$ within two versions of the Migdal-Kadanoff (MK) renormalization group procedure. One of the MK versions gives results for $f(R)$ in d=3 in reasonable agreement with those of the Monte Carlo simulations at the values of R for which they can be compared. If there were a de Almeida-Thouless (AT) line for $d \\le 6$ it would appear as a zero of the function $f(R)$ at some negative value of R, but there is no evidence for such behavior. This is consistent with the arguments that there should be no AT line for $d \\le 6$, which we review.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-08T05:02:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "75.10.Nr",
      "75.40.Cx",
      "05.50.+q",
      "75.50.Lk"
    ],
    "keywords": [
      "critical point scaling",
      "ising spin glasses",
      "magnetic field",
      "monte carlo simulations",
      "renormalization group procedure"
    ],
    "publication": {
      "doi": "10.1103/PhysRevB.91.104432",
      "journal": "Physical Review B",
      "year": 2015,
      "month": "Mar",
      "volume": 91,
      "number": 10,
      "pages": 104432
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015PhRvB..91j4432Y"
    }
  }
}