Percolation thresholds on 2D Voronoi networks and Delaunay triangulations
Abstract
The site percolation threshold for the random Voronoi network is determined numerically for the first time, with the result p_c = 0.71410 +/- 0.00002, using Monte-Carlo simulation on periodic systems of up to 40000 sites. The result is very close to the recent theoretical estimate p_c = 0.7151 of Neher, Mecke, and Wagner. For the bond threshold on the Voronoi network, we find p_c = 0.666931 +/- 0.000005, implying that for its dual, the Delaunay triangulation, p_c = 0.333069 +/- 0.000005. These results rule out the conjecture by Hsu and Huang that the bond thresholds are 2/3 and 1/3 respectively, but support the conjecture of Wierman that for fully triangulated lattices other than the regular triangular lattice, the bond threshold is less than 2 sin pi/18 = 0.3473.
Keywords
Cite
@article{arxiv.0906.4360,
title = {Percolation thresholds on 2D Voronoi networks and Delaunay triangulations},
author = {Adam M. Becker and Robert M. Ziff},
journal= {arXiv preprint arXiv:0906.4360},
year = {2009}
}
Comments
Paper split into two and additional simulations to quantify errors added