{
  "id": "1510.01718",
  "version": "v1",
  "published": "2015-10-06T19:37:26.000Z",
  "updated": "2015-10-06T19:37:26.000Z",
  "title": "Avalanches and perturbation theory in the random-field Ising model",
  "authors": [
    "Gilles Tarjus",
    "Matthieu Tissier"
  ],
  "comment": "7 pages, 9 figures",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "Perturbation theory for the random-field Ising model (RFIM) has the infamous attribute that it predicts at all orders a dimensional-reduction property for the critical behavior that turns out to be wrong in low dimension. Guided by our previous work based on the nonperturbative functional renormalization group (NP-FRG), we show that one can still make some use of the perturbation theory for a finite range of dimension below the upper critical dimension, d=6. The new twist is to account for the influence of large-scale zero-temperature events known as avalanches. These avalanches induce nonanalyticities in the field dependence of the correlation functions and renormalized vertices, and we compute in a loop expansion the eigenvalue associated with the corresponding anomalous operator. The outcome confirms the NP-FRG prediction that the dimensional-reduction fixed point correctly describes the dominant critical scaling of the RFIM above some dimension close to 5 but not below.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-06T19:37:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random-field ising model",
      "perturbation theory",
      "avalanches induce nonanalyticities",
      "large-scale zero-temperature events",
      "nonperturbative functional renormalization group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151001718T"
    }
  }
}