EVIDENCE FOR NONUNIVERSAL EXPONENTS IN BOOTSTRAP PERCOLATION

Bootstrap percolation (BP) models are systems where sites are initially randomly occupied. Those sites that do not maintain a suitable local environment of at least m occupied sites are successively removed. Current open questions concerning these systems now focus on the universality of critical exponents for the lower m values. Simulations indicate that for m=3 on the simple cubic lattice, the exponent beta which characterizes the critical behaviour of the percolation probability, is distinct from that of usual random percolation (m=0). The authors quote pc=0.5717+or-0.0005 and beta =0.6+or-0.1 for m=3. They argue that the connectivity exponent nu for m=2 should be the same as that of usual random percolation and within the limits of numerical accuracy the authors observe that this appears to be the case for m=3 on the simple cubic lattice. The implications of this surprising dichotomy are considered.