Bond percolation on a dilute lattice with short and long range correlations: A numerical simulation

The quenched percolation problem on a dilute lattice with a given random structure of vacancies is analyzed by numerical simulations in d=2 and d=3. The distribution of the sites of the dilute lattice satisfies the static structure factor S(k)=ak(-2)+b and contains short range (a=0) and long range (a much greater than 0) effects, respectively. The numerical simulation shows that the critical behavior of the percolation on lattices with short range correlations (a=0) is equivalent to the usual percolation on a regular lattice, whereas the percolation on a lattice with long range correlations shows a characteristic change of the universality class. In particular, a critical exponent beta was detected, which is significantly greater than the usual exponent beta(random).