{
  "id": "1810.07826",
  "version": "v1",
  "published": "2018-10-17T22:46:11.000Z",
  "updated": "2018-10-17T22:46:11.000Z",
  "title": "Dynamics around the Site Percolation Threshold on High-Dimensional Hypercubic Lattices",
  "authors": [
    "Giulio Biroli",
    "Patrick Charbonneau",
    "Yi Hu"
  ],
  "comment": "12 pages, 6 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Recent advances on the glass problem motivate reexamining classical models of percolation. Here, we consider the displacement of an ant in a labyrinth near the percolation threshold on cubic lattices both below and above the upper critical dimension of simple percolation, d_u=6. Using theory and simulations, we consider the scaling regime part, and obtain that both caging and subdiffusion scale logarithmically for d >= d_u. The theoretical derivation considers Bethe lattices with generalized connectivity and a random graph model, and employs a scaling analysis to confirm that logarithmic scalings should persist in the infinite dimension limit. The computational validation employs accelerated random walk simulations with a transfer-matrix description of diffusion to evaluate directly the dynamical critical exponents below d_u as well as their logarithmic scaling above d_u. Our numerical results improve various earlier estimates and are fully consistent with our theoretical predictions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-17T22:46:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "high-dimensional hypercubic lattices",
      "site percolation threshold",
      "accelerated random walk simulations",
      "validation employs accelerated random",
      "employs accelerated random walk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}