PRECISE DETERMINATION OF THE CRITICAL THRESHOLD AND EXPONENTS IN A 3-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 vario us effective percolation thresholds, we obtain a value of p(c) = 0.289 5 +/- 0.0005. This value is significantly smaller than the values obta ined for simulations that have been. carried out using smaller systems . Employing this value of p(c) and systems of size L = 160 (relative t o a sphere of unit radius), we also obtain estimates of the critical e xponents upsilon, beta, and gamma for the continuum system and show th at the values are different than those obtained using previous values of p(c).