Correlated site-bond percolation on a square lattice

A percolation model is studied, on a square lattice, with computer simulations. The sites and bonds distributions overlap and introduce correlations between sites and bonds. The percolation thresholds have been evaluated numerically. Percolation becomes easier as the correlation increases. The percolation probability (i.e. the percolating cluster mass) shows a change in its behaviour as the correlation changes. For low correlation it grows monotonically but for large correlations it shows a maximum. Similar characteristics have previously been found on a Bethe lattice.