{
  "id": "1709.00364",
  "version": "v1",
  "published": "2017-09-01T15:30:28.000Z",
  "updated": "2017-09-01T15:30:28.000Z",
  "title": "On superuniversality in the $q$-state Potts model with quenched disorder",
  "authors": [
    "Gesualdo Delfino",
    "Elena Tartaglia"
  ],
  "comment": "17 pages, 4 figures",
  "categories": [
    "cond-mat.stat-mech",
    "hep-th"
  ],
  "abstract": "We obtain the exact scale invariant scattering solutions for two-dimensional field theories with replicated permutational symmetry $\\mathbb{S}_q$. After sending to zero the number of replicas they correspond to the renormalization group fixed points of the $q$-state Potts model with quenched disorder. We find that all solutions with non-zero disorder possess $q$-independent sectors, pointing to superuniversality (i.e. symmetry independence) of some critical exponents. The solution corresponding to the random bond ferromagnet, for which disorder vanishes as $q\\to 2$, allows for superuniversality of the correlation length exponent $\\nu$ [PRL 118 (2017) 250601]. Of the two solutions which are strongly disordered for all values of $q$, one is completely $q$-independent and accounts for the zero-temperature percolation fixed point of the randomly bond diluted ferromagnet. The other is the main candidate to describe the Nishimori-like fixed point of the Potts model with $\\pm J$ disorder, and points to superuniversality of the magnetic exponent $\\eta$. Available numerical data are consistent with the latter scenario but not conclusive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-01T15:30:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "state potts model",
      "quenched disorder",
      "superuniversality",
      "exact scale invariant scattering solutions",
      "correlation length exponent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}