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 10⁵ 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 ν, β, and γ for the continuum system and show that the values are different than those obtained using previous values of p_c.