  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.
