{
  "id": "1609.02054",
  "version": "v1",
  "published": "2016-09-07T16:32:47.000Z",
  "updated": "2016-09-07T16:32:47.000Z",
  "title": "Ensemble inequivalence in a Blume-Capel model on long-range random networks",
  "authors": [
    "Levon Chakhmakhchyan",
    "Tarcisio N. Teles",
    "Stefano Ruffo"
  ],
  "comment": "5 pages, 4 figures. Submitted",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Ensemble inequivalence has been previously displayed only for long-range interacting systems with a non-extensive energy. In order to perform the thermodynamic limit, such systems require an unphysical, so-called, Kac rescaling of the coupling constant. We here propose a Blume-Capel model defined on long-range random networks, which allows one to avoid such a rescaling. Namely, the proposed model has an extensive energy, which is however non-additive. Specifically, for long-range random networks pairs of sites are coupled with a probability that decays with the distance $r$ as $1/r^\\delta$, and if $0 \\leq \\delta <1$ the surface energy of the system scales linearly with the network size, while for $\\delta >1$ it is $O(1)$. By performing numerical simulations independently in the canonical and microcanonical ensembles, we show that a negative specific heat region is present within the microcanonical description of the model, in correspondence with a first-order phase transition within the canonical ensemble. This proves that ensemble inequivalence is a consequence of non-additivity rather than non-extensivity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-07T16:32:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ensemble inequivalence",
      "blume-capel model",
      "long-range random networks pairs",
      "negative specific heat region",
      "first-order phase transition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}