Effects of site dilution on the one-dimensional long-range bond-percolation problem

The effects of the dilution of sites (with an occupancy probability ps for an active site) on the long-range bond-percolation problem, on a linear chain (d=1), are analyzed by means of a Monte Carlo simulation. The occupancy probability for a bond between two active sites i and j, separated by a distance rij is given by pij=p/rijα (α⩾0), where p represents the usual occupancy probability between nearest-neighbor sites. The percolation order parameter, P∞, is investigated numerically for different values of α and ps, in such a way that a crossover between a nonextensive regime and an extensive regime is observed.