Combined site and bond percolation with nearest- and next-nearest-neighbour bonds

Abstract

Percolation on a square lattice, in which there exist different occupation probabilities for sites, nearest-neighbour bonds and next-nearest-neighbour bonds, is studied by a real-space renormalization technique. The critical surface is controlled by a single fixed point, in accordance with universality. The critical probability for site percolation on the square lattice with diagonal bonds present, is estimated to be p ̃ c =0.41 , in agreement with series estimates.