{
  "abstract": "Using MC simulations based on an efficient single-cluster growth algorithm, we investigate two types of three-dimensional extended-range percolation models, namely cubic and complex (non-compact) neighborhoods. We obtain high-precision percolation thresholds $p_c$ for approximately 100 distinct structures and further explore the relationship between these thresholds and the topology of the lattices, which includes the total coordination number $z$, the number of sites $z_i$ and these sites' distance to the central site $r_i$ of the given neighborhood in the $i$th coordination zone. Both bond and site percolation are analyzed for cubic neighborhoods on the SC lattice. For bond percolation, the asymptotic value of $zp_c$ tends to Bethe-lattice behavior ($zp_c\\sim1$), and finite-$z$ correction is found to be consistent with $zp_{c}-1\\sim a_{1}z^{-x}$, where $x=(d-1)/d$. For site percolation, the value of $zp_c$ varies non-monotonically, exhibiting an initial increase followed by a decrease with the coordination number $z$. Linear fitting leads to $zp_c\\sim2.5987(1)$ for large $z$, predicting a value of continuum percolation threshold of aligned cubes $η_c=0.324838(12)$ using $zp_c=2^{d}η_c$. We then examine site percolation for non-compact neighborhoods extending to the fifth coordination zone on SC, FCC, and BCC lattices. Through a comparison of the three indices of $z$, $ξ=\\sum_iz_ir_i^2/i$, and $ζ=\\sum_iz_ir_i$, we find that $ζ$ is effective in removing the degeneracy. The results obtained show power-law dependence $p_c\\propto(ζ/K)^{-γ}$ with $γ_{\\mathrm{SC}}^ζ=0.703(12)$, $γ_{\\mathrm{FCC}}^ζ=0.728(10)$, and $γ_{\\mathrm{BCC}}^ζ=0.699(12)$ for SC, FCC, and BCC lattices, and $p_c\\proptoζ^{-γ}$ with $γ^ζ=0.719(9)$ independent of the underlying lattice. The number $K$ indicates lattice connectivity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15441",
  "author_total": 5,
  "authors": [
    {
      "name": "Zhe Zhang"
    },
    {
      "name": "Yuxuan Fan"
    },
    {
      "name": "Yang Yang"
    },
    {
      "name": "Yusong Tu"
    },
    {
      "name": "Zhipeng Xun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4y5nk73qxxxpw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15441",
  "fulltext_url": null,
  "id": "4y5nk73qxxxpw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15441",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7221764924",
  "pdf_url": "https://arxiv.org/pdf/2610.15441",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4y5nk73qxxxpw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.15441",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15441"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Extended-range percolation on lattices with cubic and non-compact neighborhoods in three dimensions",
  "title_text": "Extended-range percolation on lattices with cubic and non-compact neighborhoods in three dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:06Z",
  "url": "https://research.draconitic.com/paper/4y5nk73qxxxpw",
  "venue": "arXiv",
  "versions": []
}