{
  "id": "1807.08739",
  "version": "v1",
  "published": "2018-07-23T17:35:48.000Z",
  "updated": "2018-07-23T17:35:48.000Z",
  "title": "Universality class of explosive percolation in Barabási-Albert networks",
  "authors": [
    "M. Habib-E-Islam",
    "M. K. Hassan"
  ],
  "comment": "8 pages, 7 captioned figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "In this work, we study explosive percolation (EP) in Barab\\'{a}si-Albert (BA) network, in which nodes are born with degree $k=m$, for both product rule (PR) and sum rule (SR) of the Achlioptas process. For $m=1$ we find that the critical point $t_c=1$ which is the maximum possible value of the relative link density $t$; Hence we cannot have access to the other phase like percolation in one dimension. However, for $m>1$ we find that $t_c$ decreases with increasing $m$ and the critical exponents $\\nu, \\alpha, \\beta$ and $\\gamma$ for $m>1$ are found to be independent not only of the value of $m$ but also of PR and SR. It implies that they all belong to the same universality class like EP in the Erd\\\"{o}s-R\\'{e}nyi network. Besides, the critical exponents obey the Rushbrooke inequality in the form $\\alpha+2\\beta+\\gamma=2+\\epsilon$ with $0<\\epsilon<<1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-23T17:35:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "universality class",
      "barabási-albert networks",
      "product rule",
      "study explosive percolation",
      "sum rule"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}