{
  "abstract": "We study Bernoulli percolation and its universality classes on hierarchical lattices generated by edge iterated graph systems (EIGS). By examining eight critical exponents, we prove that no finite family of substitution-multiplicative dimensions completely determines universality, providing a rigorous proof of the failure of dimension-based universality discussed by Hauser and Saxena [Phys. Rev. B 34 (1986), 8193-8195]. Although the six exponentials theorem provides number-theoretic criteria for scale commensurability, we further disprove the conjecture that critical-exponent universality requires commensurate discrete renormalisation scales.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10469",
  "author_total": 1,
  "authors": [
    {
      "name": "Ziyu Neroli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/97sn6s9dc0q88.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10469",
  "fulltext_url": null,
  "id": "97sn6s9dc0q88",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10469",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
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      "arxiv",
      "math-ph"
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      "arxiv",
      "math.MP"
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      "math.PR"
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      "3104|Theoretical and Computational Physics"
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  "openalex": "W7221057845",
  "pdf_url": "https://arxiv.org/pdf/2610.10469",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/97sn6s9dc0q88.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2610.10469",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10469"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Iterated Graph Systems (II): Bernoulli percolation and critical-exponent universality classes on hierarchical lattices",
  "title_text": "Iterated Graph Systems (II): Bernoulli percolation and critical-exponent universality classes on hierarchical lattices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/97sn6s9dc0q88",
  "venue": "arXiv",
  "versions": []
}