Precise determination of the void percolation threshold for two distributions of overlapping spheres

The void percolation threshold is calculated for a distribution of overlapping spheres with equal radii, and for a binary-sized distribution of overlapping spheres, where half of the spheres have radii twice as large as the other half. Using systems much larger than previous work, we determine a much more precise value for the percolation thresholds and correlation length exponent. The value of the percolation threshold for the monodisperse case is shown to be 0. 0301+/-0.0003, whereas the value for the bidisperse case is shown to be p(c)=0.0287+/-0.0005. The fact that these are significantly different is in contrast with previous, less precise works that speculated that the threshold might be universal with respect to sphere size distribution.