{
  "id": "1512.03635",
  "version": "v1",
  "published": "2015-12-11T13:39:31.000Z",
  "updated": "2015-12-11T13:39:31.000Z",
  "title": "Marginal dimensions of the Potts model with invisible states",
  "authors": [
    "M. Krasnytska",
    "P. Sarkanych",
    "B. Berche",
    "Yu. Holovatch",
    "R. Kenna"
  ],
  "comment": "15 pages, 7 figures, 2 tables",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We reconsider the mean-field Potts model with $q$ interacting and $r$ non-interacting (invisible) states. The model was recently introduced to explain discrepancies between theoretical predictions and experimental observations of phase transitions in some systems where the $Z_q$-symmetry is spontaneously broken. We analyse the marginal dimensions of the model, i.e., the value of $r$ at which the order of the phase transition changes. In the $q=2$ case, we determine that value to be $r_c = 3.65(5)$; there is a second-order phase transition there when $r<r_c$ and a first-order one at $r>r_c$. We also analyse the region $1 \\leq q<2$ and show that the change from second to first order there is manifest through a new mechanism involving {\\emph{two}} marginal values of $r$. The $q=1$ limit gives bond percolation and some intermediary values also have known physical realisations. Above the lower value $r_{c1}$, the order parameters exhibit discontinuities at temperature $\\tilde{t}$ below a critical value $t_c$. But, provided $r>r_{c1}$ is small enough, this discontinuity does not appear at the phase transition, which is continuous and takes place at $t_c$. The larger value $r_{c2}$ marks the point at which the phase transition at $t_c$ changes from second to first order. Thus, for $r_{c1}< r < r_{c2}$, the transition at $t_c$ remains second order while the order parameter has a discontinuity at $\\tilde{t}$. As $r$ increases further, $\\tilde{t}$ increases, bringing the discontinuity closer to $t_c$. Finally, when $r$ exceeds $r_{c2}$ $\\tilde{t}$ coincides with $t_c$ and the phase transition becomes first order. This new mechanism indicates how the discontinuity characteristic of first order phase transitions emerges.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-11T13:39:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "potts model",
      "marginal dimensions",
      "invisible states",
      "discontinuity",
      "first order phase transitions emerges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151203635K"
    }
  }
}