Monte Carlo renormalisation group study of bootstrap percolation

The authors develop a Monte Carlo position space renormalisation group method to study the scaling properties of bootstrap percolation. In this model sites on a lattice are randomly occupied with probability p and sites with less than m occupied neighbours are culled until a stable configuration remains. Using progressively larger length rescaling factors b, they obtain numerical results on the triangular lattice for the percolation threshold p c (b), the connectedness length exponent nu (b) and the fractal dimension d f (b). The large b limit yields numerical values of d f for m=2 and 3 which are consistent with d f for ordinary percolation (m=0). Although the small b dependence of nu for m=2 and 3 is qualitatively different from that of ordinary percolation, the large b behaviour of nu suggests that m=2 and m=3 bootstrap percolation on the triangular lattice are in the same universality class as ordinary percolation.