Abstract
The consequences of Schonmann's new proof that the critical threshold is unity for certain bootstrap percolation models are explored. It is shown that this proof provides an upper bound for the finite-size scaling in these systems. Comparison 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 sizeL scales asO[ln(lnL)] for the isotropic model in three dimensions where sites that fail to have at least four neighbors are culled.
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Related systems have been studied in the context of cellular automata.(4)
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van Enter, A.C.D., Adler, J. & Duarte, J.A.M.S. Finite-size effects for some bootstrap percolation models. J Stat Phys 60, 323–332 (1990). https://doi.org/10.1007/BF01314923
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DOI: https://doi.org/10.1007/BF01314923