Precise determination of the critical threshold and exponents in a three-dimensional continuum percolation model

. We present a large-scale computer simulation of the prototypical three-dimensional continuum percolation model consisting of a distribution of overlapping (spatially uncorrelated) spheres. By using simulations of up to 10 5 particles and studying the finite-size scaling of various effective percolation thresholds, we obtain a value of p c = 0.2895 0.0005. This value is significantly smaller than the values obtained for simulations that have been carried out using smaller systems. Employing this value of p c and systems of size L = 160 (relative to a sphere of unit radius), we also obtain estimates of the critical exponents #, #, and # for the continuum system and show that the values are different than those obtained using previous values of p c . 1. Introduction Continuum percolation studies have become increasingly common in the literature, as they contain many of the same interesting mathematical properties of lattice percolation and often are more realistic models of a v...