A.C.D.: Finite-size effects for some bootstrap percolation models

The consequences of Schonmann's new proof that the critical threshold is unity for certain bootstrap ercolation models are explored. It is shown that this proof provides an upper bound for the finite-size scaling in these systems. Com-parison with data for one case demonstrates that this scaling appears to give the correct asymptotics. We show that the threshold for a finite system of size L scales as O{1/[ln(ln L)]} for the isotropic model in three dimensions where sites that fail to have at least four neighbors are culled. KEY WORDS: Bootstrap percolation; critical exponents; phase transition; finite-size scaling; simulation