{
  "id": "1205.5884",
  "version": "v1",
  "published": "2012-05-26T13:38:48.000Z",
  "updated": "2012-05-26T13:38:48.000Z",
  "title": "Percolation transitions with nonlocal constraint",
  "authors": [
    "Pyoung-Seop Shim",
    "Hyun Keun Lee",
    "Jae Dong Noh"
  ],
  "comment": "4 pages, 5 figures",
  "journal": "Phys. Rev. E 86, 031113 (2012)",
  "doi": "10.1103/PhysRevE.86.031113",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We investigate percolation transitions in a nonlocal network model numerically. In this model, each node has an exclusive partner and a link is forbidden between two nodes whose $r$-neighbors share any exclusive pair. The $r$-neighbor of a node $x$ is defined as a set of at most $N^r$ neighbors of $x$, where $N$ is the total number of nodes. The parameter $r$ controls the strength of a nonlocal effect. The system is found to undergo a percolation transition belonging to the mean field universality class for $r< 1/2$. On the other hand, for $r>1/2$, the system undergoes a peculiar phase transition from a non-percolating phase to a quasi-critical phase where the largest cluster size $G$ scales as $G \\sim N^{\\alpha}$ with $\\alpha = 0.74 (1)$. In the marginal case with $r=1/2$, the model displays a percolation transition that does not belong to the mean field universality class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-26T13:38:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "64.60.aq",
      "64.60.ah",
      "05.70.Fh"
    ],
    "keywords": [
      "percolation transition",
      "mean field universality class",
      "nonlocal constraint",
      "nonlocal network model",
      "peculiar phase transition"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2012,
      "month": "Sep",
      "volume": 86,
      "number": 3,
      "pages": "031113"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012PhRvE..86c1113S"
    }
  }
}