{
  "id": "1103.4439",
  "version": "v3",
  "published": "2011-03-23T05:29:25.000Z",
  "updated": "2011-06-16T02:36:03.000Z",
  "title": "Continuity of the Explosive Percolation Transition",
  "authors": [
    "Hyun Keun Lee",
    "Beom Jun Kim",
    "Hyunggyu Park"
  ],
  "comment": "Some corrections during the review",
  "journal": "Phys. Rev. E 84, 020101(R) (2011)",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is found to be well described by the power-law form with the decay exponent $\\tau = 2.06(2)$, followed by a hump. We then use the finite-size scaling method to make all the distributions at various system sizes up to $N=2^{37}$ collapse perfectly onto a scaling curve characterized solely by the single exponent $\\tau$. We also observe that the instant of that collapse converges to a well-defined percolation threshold from below as $N\\rightarrow\\infty$. Based on these observations, we show that the explosive percolation transition in the model should be continuous, contrary to the widely-spread belief of its discontinuity.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-06-16T02:36:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "64.60.ah",
      "36.40.Ei",
      "64.60.aq"
    ],
    "keywords": [
      "explosive percolation transition",
      "continuity",
      "distribution",
      "complete graph",
      "widely-spread belief"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "doi": "10.1103/PhysRevE.84.020101",
      "year": 2011,
      "month": "Aug",
      "volume": 84,
      "number": 2,
      "pages": "020101"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PhRvE..84b0101L"
    }
  }
}