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PreprintCC BY 4.0arXiv

Iterated Graph Systems (II): Bernoulli percolation and critical-exponent universality classes on hierarchical lattices

  • Ziyu Neroli
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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.

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Cite

BibTeXRIS
BibTeX
@misc{neroli2026iterated,
  title = {{Iterated Graph Systems (II): Bernoulli percolation and critical-exponent universality classes on hierarchical lattices}},
  author = {Ziyu Neroli},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10469},
  eprint = {2610.10469},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10469},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Iterated Graph Systems (II): Bernoulli percolation and critical-exponent universality classes on hierarchical lattices
AU  - Ziyu Neroli
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10469
UR  - https://arxiv.org/abs/2610.10469
AB  - 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.
ER  -