{
  "id": "0811.3827",
  "version": "v1",
  "published": "2008-11-24T09:36:47.000Z",
  "updated": "2008-11-24T09:36:47.000Z",
  "title": "Ising model on the Apollonian network with node dependent interactions",
  "authors": [
    "R. F. S. Andrade",
    "J. S. Andrade Jr.",
    "H. J. Herrmann"
  ],
  "comment": "6 figures, 12 figure files",
  "doi": "10.1103/PhysRevE.79.036105",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "This work considers an Ising model on the Apollonian network, where the exchange constant $J_{i,j}\\sim1/(k_ik_j)^\\mu$ between two neighboring spins $(i,j)$ is a function of the degree $k$ of both spins. Using the exact geometrical construction rule for the network, the thermodynamical and magnetic properties are evaluated by iterating a system of discrete maps that allows for very precise results in the thermodynamic limit. The results can be compared to the predictions of a general framework for spins models on scale-free networks, where the node distribution $P(k)\\sim k^{-\\gamma}$, with node dependent interacting constants. We observe that, by increasing $\\mu$, the critical behavior of the model changes, from a phase transition at $T=\\infty$ for a uniform system $(\\mu=0)$, to a T=0 phase transition when $\\mu=1$: in the thermodynamic limit, the system shows no exactly critical behavior at a finite temperature. The magnetization and magnetic susceptibility are found to present non-critical scaling properties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-24T09:36:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "89.75.Hc",
      "05.50.+q",
      "64.60.aq"
    ],
    "keywords": [
      "node dependent interactions",
      "apollonian network",
      "ising model",
      "thermodynamic limit",
      "phase transition"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2009,
      "month": "Mar",
      "volume": 79,
      "number": 3,
      "pages": "036105"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009PhRvE..79c6105A"
    }
  }
}