Percolation on Isotropically Directed Lattice
Disordered Systems and Neural Networks
2018-12-19 v2 Statistical Mechanics
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.
Cite
@article{arxiv.1808.06644,
title = {Percolation on Isotropically Directed Lattice},
author = {Aurelio W. T. de Noronha and André A. Moreira and André P. Vieira and Hans J. Herrmann and José S. Andrade and Humberto A. Carmona},
journal= {arXiv preprint arXiv:1808.06644},
year = {2018}
}
Comments
10 pages, 11 figures