{
  "id": "1510.00534",
  "version": "v1",
  "published": "2015-10-02T09:11:15.000Z",
  "updated": "2015-10-02T09:11:15.000Z",
  "title": "Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks",
  "authors": [
    "M. Krasnytska",
    "B. Berche",
    "Yu. Holovatch",
    "R. Kenna"
  ],
  "comment": "36 pages, 31 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "We analyze the partition function of the Ising model on graphs of two different types: complete graphs, wherein all nodes are mutually linked and annealed scale-free networks for which the degree distribution decays as $P(k)\\sim k^{-\\lambda}$. We are interested in zeros of the partition function in the cases of complex temperature or complex external field (Fisher and Lee-Yang zeros respectively). For the model on an annealed scale-free network, we find an integral representation for the partition function which, in the case $\\lambda > 5$, reproduces the zeros for the Ising model on a complete graph. For $3<\\lambda < 5$ we derive the $\\lambda$-dependent angle at which the Fisher zeros impact onto the real temperature axis. This, in turn, gives access to the $\\lambda$-dependent universal values of the critical exponents and critical amplitudes ratios. Our analysis of the Lee-Yang zeros reveals a difference in their behaviour for the Ising model on a complete graph and on an annealed scale-free network when $3<\\lambda <5$. Whereas in the former case the zeros are purely imaginary, they have a non zero real part in latter case, so that the celebrated Lee-Yang circle theorem is violated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-02T09:11:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "annealed scale-free network",
      "complete graph",
      "ising model",
      "partition function zeros",
      "non zero real part"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/49/13/135001",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2016,
      "month": "Apr",
      "volume": 49,
      "number": 13,
      "pages": 135001
    },
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016JPhA...49m5001K"
    }
  }
}