Percolation on Growing Lattices

TL;DR

This paper introduces a modified Hoshen-Kopelman algorithm enabling efficient simulation of growing lattices to study percolation properties across various sizes and occupation probabilities in three dimensions.

Contribution

It presents a novel algorithm that allows simultaneous simulation of multiple lattice sizes, improving efficiency in percolation studies.

Findings

Simulated lattices up to size 5000 in 3D

Analyzed percolation at multiple occupation probabilities

Provided data on size dependence of percolation observables

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.