Strongly-connected percolation on directed lattices

M. E. J. Newman; P. Grassberger; R. M. Ziff

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arXiv · 2607.24975

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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M. E. J. Newman, P. Grassberger, R. M. Ziff. 2026-07-27. Strongly-connected percolation on directed lattices. https://arxiv.org/abs/2607.24975

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