{
  "id": "1610.06786",
  "version": "v1",
  "published": "2016-10-21T13:58:06.000Z",
  "updated": "2016-10-21T13:58:06.000Z",
  "title": "Disorder relevance without Harris Criterion: the case of pinning model with $γ$-stable environment",
  "authors": [
    "Hubert Lacoin",
    "Julien Sohier"
  ],
  "comment": "25 Pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We investigate disorder relevance for the pinning of a renewal whose inter-arrival law has tail exponent $\\alpha>0$ when the law of the random environment is in the domain of attraction of a stable law with parameter $\\gamma \\in (1,2)$. We prove that in this case, the effect of disorder is not decided by the sign of the specific heat exponent as predicted by Harris criterion but that a new criterion emerges to decide disorder relevance. More precisely we show that when $\\alpha>1-\\gamma^{-1}$ there is a shift of the critical point at every temperature whereas when $\\alpha< 1-\\gamma^{-1}$, at high temperature the quenched and annealed critical point coincide, and the critical exponents are identical.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-21T13:58:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K37",
      "82B27",
      "82B44"
    ],
    "keywords": [
      "harris criterion",
      "stable environment",
      "pinning model",
      "critical point",
      "decide disorder relevance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}