Simple Cubic Random-Site Percolation Thresholds for Complex Neighbourhoods

In this communication by means of computer simulation we evaluate simple cubic random-site percolation thresholds for neighbourhoods including the nearest neighbours (NN), the next-nearest neighbours (2NN) and the next-next-nearest neighbours (3NN). Our estimations base on finite-size scaling analysis of the percolation probability vs. site occupation probability plots. The Hoshen–Kopelman algorithm has been applied for cluster labelling. The calculated thresholds are 0.1372(1), 0.1420(1), 0.0976(1), 0.1991(1), 0.1036(1), 0.2455(1) for (NN + 2NN), (NN + 3NN), (NN + 2NN + 3NN), 2NN, (2NN + 3NN), 3NN neighbourhoods, respectively. In contrast to the results obtained for a square lattice the calculated percolation thresholds decrease monotonically with the site coordination number z, at least for our inspected neighbourhoods.