Invariant properties of the percolation thresholds in the soft-core<i>–</i>hard-core transition

Abstract

We report the first Monte Carlo study of the average critical number of bonds per site ${B}_{c}$ for three-dimensional continuum systems. The results show that for a system of spheres the dependence of ${B}_{c}$ on the soft-shell to hard-core ratio can be mapped onto the site-percolation--bond-percolation transition in lattices. For a system of very long cylinders, ${B}_{c}$ appears to be a dimensional invariant. It is predicted that for any continuum system the above dependence will be equal or weaker than that of a system of spheres.