{
  "id": "2006.15621",
  "version": "v1",
  "published": "2020-06-28T14:35:52.000Z",
  "updated": "2020-06-28T14:35:52.000Z",
  "title": "Site percolation thresholds on triangular lattice with complex neighborhoods",
  "authors": [
    "Krzysztof Malarz"
  ],
  "comment": "5 pages with 3 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We determine thresholds $p_c$ for random site percolation on triangular lattice for neighborhoods containing nearest (NN), next-nearest (2NN) and next-next-nearest (3NN) neighbors, and their combinations (2NN+NN, 3NN+NN, 3NN+2NN, 3NN+2NN+NN). We use a fast Monte Carlo algorithm, by Newman--Ziff, for obtaining the dependence of the largest cluster size on occupation probability. The method is combined with a method, by Bastas et al., of estimating thresholds from low statistics data. The estimated values of percolation thresholds are $\\hat p_c(\\text{2NN})=0.232020(36)$, $\\hat p_c(\\text{3NN})=0.140250(36)$, $\\hat p_c(\\text{2NN+NN})=0.215459(36)$, $\\hat p_c(\\text{3NN+NN})=0.131660(36)$, $\\hat p_c(\\text{3NN+2NN})=0.117460(36)$, $\\hat p_c(\\text{3NN+2NN+NN})= 0.115740(36)$. The method is tested on the standard case of site percolation on triangular lattice, where $p_c(\\text{NN})=\\frac{1}{2}$ is recovered with five digits accuracy $\\hat p_c(\\text{NN})=0.499971(36)$ by averaging over thousand lattice realizations only.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-28T14:35:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "triangular lattice",
      "site percolation thresholds",
      "complex neighborhoods",
      "fast monte carlo algorithm",
      "random site percolation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}