Percolation thresholds on two-dimensional Voronoi networks and Delaunay triangulations

The site percolation threshold for the random Voronoi network is determined numerically, with the result p(c)=0.714 10 +/- 0.000 02, using Monte Carlo simulation on periodic systems of up to 40 000 sites. The result is very close to the recent theoretical estimate p(c)approximate to 0.7151 of Neher For the bond threshold on the Voronoi network, we find p(c)=0.666 931 +/- 0.000 005 implying that, for its dual, the Delaunay triangulation p(c)=0.333 069 +/- 0.000 005. 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 approximate to 0.3473.