Bootstrap and diffusion percolation transitions in three-dimensional lattices

Abstract

We study the bootstrap and diffusion percolation models in the simple-cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices using the Newman–Ziff algorithm. The percolation threshold and critical exponents were calculated through finite-size scaling with high precision in the three lattices. In addition to the continuous and first-order percolation transitions, we found a double transition, which is a continuous transition followed by a discontinuity of the order parameter. We show that the continuous transitions of the bootstrap and diffusion percolation models have the same critical exponents as the classical percolation within error bars and they all belong to the same universality class.