{
  "id": "cond-mat/0412355",
  "version": "v1",
  "published": "2004-12-14T11:42:20.000Z",
  "updated": "2004-12-14T11:42:20.000Z",
  "title": "Ising model in scale-free networks: A Monte Carlo simulation",
  "authors": [
    "Carlos P. Herrero"
  ],
  "comment": "5 pages, 5 figures",
  "journal": "Phys. Rev. E 69, 067109 (2004)",
  "doi": "10.1103/PhysRevE.69.067109",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The Ising model in uncorrelated scale-free networks has been studied by means of Monte Carlo simulations. These networks are characterized by a degree (or connectivity) distribution $P(k) \\sim k^{-\\gamma}$. The ferromagnetic-paramagnetic transition temperature has been studied as a function of the parameter $\\gamma$. For $\\gamma > 3$ our results agree with earlier analytical calculations, which found a phase transition at a temperature $T_c(\\gamma)$ in the thermodynamic limit. For $\\gamma \\leq 3$, a ferromagnetic-paramagnetic crossover occurs at a size-dependent temperature $T_{co}$, and the system is in the ordered ferromagnetic state at any temperature for a system size $N \\to \\infty$. For $\\gamma = 3$ and large enough $N$, the crossover temperature is found to be $T_{co} \\approx A \\ln N$, with a prefactor $A$ proportional to the mean degree. For $2 < \\gamma < 3$, we obtain $T_{co} \\sim < k > N^z$, with an exponent $z$ that decreases as $\\gamma$ increases. This exponent is found to be lower than predicted by earlier calculations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-12-14T11:42:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monte carlo simulation",
      "scale-free networks",
      "ising model",
      "ferromagnetic-paramagnetic transition temperature",
      "ferromagnetic-paramagnetic crossover occurs"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}