{
  "id": "cond-mat/0306017",
  "version": "v1",
  "published": "2003-06-02T04:19:12.000Z",
  "updated": "2003-06-02T04:19:12.000Z",
  "title": "Phase transition in the Ising model on a small-world network with distance-dependent interactions",
  "authors": [
    "Daun Jeong",
    "H. Hong",
    "Beom Jun Kim",
    "M. Y. Choi"
  ],
  "journal": "Phys. Rev. E 68, 027101 (2003)",
  "doi": "10.1103/PhysRevE.68.027101",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the collective behavior of an Ising system on a small-world network with the interaction $J(r) \\propto r^{-\\alpha}$, where $r$ represents the Euclidean distance between two nodes. In the case of $\\alpha = 0$ corresponding to the uniform interaction, the system is known to possess a phase transition of the mean-field nature, while the system with the short-range interaction $(\\alpha\\to\\infty)$ does not exhibit long-range order at any finite temperature. Monte Carlo simulations are performed at various values of $\\alpha$, and the critical value $\\alpha_c$ beyond which the long-range order does not emerge is estimated to be zero. Thus concluded is the absence of a phase transition in the system with the algebraically decaying interaction $r^{-\\alpha}$ for any nonzero positive value of $\\alpha$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-06-02T04:19:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "phase transition",
      "small-world network",
      "distance-dependent interactions",
      "ising model",
      "long-range order"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}