{
  "id": "cond-mat/9903426",
  "version": "v4",
  "published": "1999-03-30T00:10:33.000Z",
  "updated": "2000-04-11T21:47:23.000Z",
  "title": "First-order transition in small-world networks",
  "authors": [
    "M. Argollo de Menezes",
    "C. Moukarzel",
    "T. J. P. Penna"
  ],
  "comment": "4 pages, 3 figures, To appear in Europhysics Letters",
  "journal": "Europhys. Lett. vol.50, 5 (2000).",
  "doi": "10.1209/epl/i2000-00308-1",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "The small-world transition is a first-order transition at zero density $p$ of shortcuts, whereby the normalized shortest-path distance undergoes a discontinuity in the thermodynamic limit. On finite systems the apparent transition is shifted by $\\Delta p \\sim L^{-d}$. Equivalently a ``persistence size'' $L^* \\sim p^{-1/d}$ can be defined in connection with finite-size effects. Assuming $L^* \\sim p^{-\\tau}$, simple rescaling arguments imply that $\\tau=1/d$. We confirm this result by extensive numerical simulation in one to four dimensions, and argue that $\\tau=1/d$ implies that this transition is first-order.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2000-04-11T21:47:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first-order transition",
      "small-world networks",
      "normalized shortest-path distance undergoes",
      "zero density",
      "apparent transition"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}