Monte-Carlo renormalisation group for continuum percolation with excluded-volume interactions

Abstract

The critical properties of a continuum percolation system with excluded-volume interactions are studied by Monte-Carlo position-space renormalisation group methods. The model system considered is comprised of oriented squares of unit side with concentric square hard-core regions of side L_hc. These elements are randomly distributed in a square planar region at a concentration x. For eight values of L_hc, the percolation threshold x* is estimated. Additionally, for two of these eight values, the connectedness-length exponent v is computed. A monotonic dependence of x* upon L_hc is observed and the estimates are close to those of the lattice and freely overlapping continuum percolation problems. However, the accuracy of these estimates is not sufficiently precise to determine whether there is universality of continuum systems with respect to the size of the hard cores.