{
  "id": "2109.15069",
  "version": "v2",
  "published": "2021-09-30T12:30:17.000Z",
  "updated": "2022-01-20T09:20:52.000Z",
  "title": "$K$-selective percolation: A simple model leading to a rich repertoire of phase transitions",
  "authors": [
    "Jung-Ho Kim",
    "K. -I. Goh"
  ],
  "comment": "10 pages, 8 figures",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech",
    "physics.soc-ph"
  ],
  "abstract": "We propose the $K$-selective percolation process as a model for the iterative removals of nodes with the specific intermediate degree in complex networks. In the model, a random node with degree $K$ is deactivated one by one until no more nodes with degree $K$ remain. The non-monotonic response of the giant component size on various synthetic and real-world networks implies a conclusion that a network can be more robust against such selective attack by removing further edges. In the theoretical perspective, the $K$-selective percolation process exhibits a rich repertoire of phase transitions, including double transitions of hybrid and continuous, as well as reentrant transitions. Notably, we observe a tricritical-like point on Erd\\H{o}s-R\\'enyi networks. We also examine a discontinuous transition with unusual order parameter fluctuation and distribution on simple cubic lattices, which does not appear in other percolation models with cascade processes. Finally, we perform finite-size scaling analysis to obtain critical exponents on various transition points, including those exotic ones.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-01-20T09:20:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "phase transitions",
      "simple model leading",
      "rich repertoire",
      "selective percolation process",
      "unusual order parameter fluctuation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}