{
  "id": "1511.06879",
  "version": "v1",
  "published": "2015-11-21T13:12:59.000Z",
  "updated": "2015-11-21T13:12:59.000Z",
  "title": "Nature of phase transitions in $F$ coupled $q$-state Potts models",
  "authors": [
    "Yerali Gandica",
    "Silvia Chiacchiera"
  ],
  "comment": "23 pages, 6 figures",
  "categories": [
    "cond-mat.stat-mech",
    "physics.soc-ph"
  ],
  "abstract": "We study $F$ coupled $q$-state Potts models in a two-dimensional square lattice. The interaction between the different layers is attractive, to favour a simultaneous alignment in all of them. The nature of the phase transition for zero field is numerically determined for $F=2,3$. Using the Lee-Kosterlitz method, we find that it is continuous for $q=2$, whereas it is abrupt for $q>2$. When a continuous phase transition takes place, we also analyze the properties of the geometrical clusters. This allows us to determine the fractal dimension $D$ of the incipient infinite cluster and to corroborate the nature of the phase transition via finite-size scaling and data collapse. A mean-field approximation of the model, from which some general trends can be determined, is presented too. Finally, since this lattice model has been recently considered as a thermodynamic counterpart of the Axelrod model of social dynamics, we discuss our results in connection with this one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-21T13:12:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "state potts models",
      "phase transition",
      "two-dimensional square lattice",
      "incipient infinite cluster",
      "zero field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}