{
  "id": "1307.2803",
  "version": "v1",
  "published": "2013-07-10T14:34:11.000Z",
  "updated": "2013-07-10T14:34:11.000Z",
  "title": "Potts Models with Invisible States on General Bethe Lattices",
  "authors": [
    "N. Ananikian",
    "N. Sh. Izmailyan",
    "D. A. Johnston",
    "R. Kenna",
    "R. P. K. C. M. Ranasinghe"
  ],
  "journal": "J. Phys. A: Math. Theor. 46 (2013) 385002",
  "doi": "10.1088/1751-8113/46/38/385002",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The number of so-called invisible states which need to be added to the q-state Potts model to transmute its phase transition from continuous to first order has attracted recent attention. In the q=2 case, a Bragg-Williams, mean-field approach necessitates four such invisible states while a 3-regular, random-graph formalism requires seventeen. In both of these cases, the changeover from second- to first-order behaviour induced by the invisible states is identified through the tricritical point of an equivalent Blume-Emery-Griffiths model. Here we investigate the generalised Potts model on a Bethe lattice with z neighbours. We show that, in the q=2 case, r_c(z)=[4 z / 3(z-1)] [(z-1)/(z-2)]^z invisible states are required to manifest the equivalent Blume-Emery-Griffiths tricriticality. When z=3, the 3-regular, random-graph result is recovered, while the infinite z limit delivers the Bragg-Williams, mean-field result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-10T14:34:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "invisible states",
      "general bethe lattices",
      "equivalent blume-emery-griffiths tricriticality",
      "q-state potts model",
      "mean-field approach necessitates"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2013,
      "month": "Aug",
      "volume": 46,
      "number": 31,
      "pages": 315002
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JPhA...46.5002A"
    }
  }
}