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PreprintarXiv licencearXiv

Strongly-connected percolation on directed lattices

  • M. E. J. Newman
  • P. Grassberger
  • R. M. Ziff
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Abstract

We study percolation on lattices with directed bonds, focusing on the behavior of strongly-connected percolation clusters -- clusters in which every site is reachable from every other along a directed path. We consider the two-dimensional square lattice and various globally isotropic arrangements of the directions of the bonds. Performing simulations using a range of algorithmic approaches, we calculate high-precision values for critical exponents, fractal dimensions, crossing probabilities, and percolation thresholds for bond percolation with each bond arrangement. We find that the critical behavior is in a distinctly different universality class from that of traditional undirected percolation, but that all bond arrangements appear to fall in the same universality class.

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Cite

BibTeXRIS
BibTeX
@misc{newman2026stronglyconnected,
  title = {{Strongly-connected percolation on directed lattices}},
  author = {M. E. J. Newman and P. Grassberger and R. M. Ziff},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2607.24975},
  eprint = {2607.24975},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.24975},
}
RIS
TY  - UNPB
TI  - Strongly-connected percolation on directed lattices
AU  - M. E. J. Newman
AU  - P. Grassberger
AU  - R. M. Ziff
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2607.24975
UR  - https://arxiv.org/abs/2607.24975
AB  - We study percolation on lattices with directed bonds, focusing on the behavior of strongly-connected percolation clusters -- clusters in which every site is reachable from every other along a directed path. We consider the two-dimensional square lattice and various globally isotropic arrangements of the directions of the bonds. Performing simulations using a range of algorithmic approaches, we calculate high-precision values for critical exponents, fractal dimensions, crossing probabilities, and percolation thresholds for bond percolation with each bond arrangement. We find that the critical behavior is in a distinctly different universality class from that of traditional undirected percolation, but that all bond arrangements appear to fall in the same universality class.
ER  -