{
  "id": "1512.06571",
  "version": "v1",
  "published": "2015-12-21T10:40:37.000Z",
  "updated": "2015-12-21T10:40:37.000Z",
  "title": "Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions",
  "authors": [
    "Nikolaos G. Fytas",
    "Victor Martin-Mayor"
  ],
  "comment": "15 pages, 9 figures, 2 tables",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "It was recently shown [Phys. Rev. Lett. {\\bf 110}, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero- and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent $\\alpha$ of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-21T10:40:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random-field ising model",
      "efficient numerical methods",
      "response functions",
      "reweighting extrapolation",
      "finite-size scaling"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151206571F"
    }
  }
}