Site percolation of a fixed lattice size with growing regions of disallowed occupancy

Abstract

We study site percolation in a rectangular lattice with increasing size of two clumped groups of banned sites. The percolation threshold was found to increase as the size of the banned sites is increased. The results were compared to the previously studied lattice with a system with a single group of clumped banned sites with the same number of available sites for occupation. It was observed that the percolation threshold for the dual case is greater than that of the single case. However, the thresholds follow the same trend as the number of available sites is increased.