Percolation on Isotropically Directed Lattice

TL;DR

This paper studies a new type of percolation on randomly directed lattices, deriving exact thresholds and identifying unique critical exponents that differ from classical models, advancing understanding of complex network connectivity.

Contribution

It provides exact percolation thresholds for planar lattices, proposes a conjecture for general thresholds, and identifies novel universal critical exponents for strongly-connected components.

Findings

Exact percolation thresholds for planar lattices.

Conjecture for percolation threshold in arbitrary lattices.

Identification of unique critical exponents differing from classical models.

Abstract

We investigate percolation on a randomly directed lattice, an intermediate between standard percolation and directed percolation, focusing on the isotropic case in which bonds on opposite directions occur with the same probability. We derive exact results for the percolation threshold on planar lattices, and present a conjecture for the value the percolation-threshold for in any lattice. We also identify presumably universal critical exponents, including a fractal dimension, associated with the strongly-connected components both for planar and cubic lattices. These critical exponents are different from those associated either with standard percolation or with directed percolation.