Percolation on Growing Lattices

Abstract

In order to investigate the dependence on lattice size of several observables in percolation, the Hoshen-Kopelman algorithm was modified so that growing lattices could be simulated. By this way, when simulating a lattice of size L, lattices of smaller sizes can be simulated in the same run for free, saving computing time. Here, site percolation in three dimensions was studied. Lattices of up to L=5000, with many L-steps in between, have been simulated, for occupation probabilities of p=0.25, p=0.3, p=p_c=0.311608, and p=0.35.