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≈0.7151 of Neher et al. 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 π/18≈0.3473.