Universality class for bootstrap percolation with m=3 on the cubic lattice

We study the m = 3 bootstrap percolation model on a cubic lattice, using Monte Carlo simulation and finite-size scaling techniques. In bootstrap percolation, sites on a lattice are considered occupied (present) or vacant (absent) with probability p or 1 - p, respectively. Occupied sites with less than m, occupied first-neighbors are then rendered unoccupied; this culling process is repeated until a stable configuration is reached. We evaluate the percolation critical probability, p(c), and both scaling powers, y(p) and y(h), and, contrary to previous calculations, our results indicate that the model belongs to the same universality class as usual percolation (i.e., m = 0). The critical spanning probability, R(p(c)), is also numerically studied for systems with linear sizes ranging from L = 32 up to L = 480; the value we found, R(p(c)) = 0.270 +/- 0.005, is the same as for usual percolation with free boundary conditions.