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Finite-size effects for some bootstrap percolation models |
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| Authors: | A C D van Enter Joan Adler J A M S Duarte |
| Institution: | (1) Institute of Theoretical Physics, RUG, Groningen, The Netherlands;(2) Department of Physics, Technion, 32000 Haifa, Israel;(3) Department of Physics and Astronomy, University of Tel Aviv, 69978 Ramat Aviv, Israel;(4) HLRZ, Jülich;(5) Institut für Theoretische Physik, 5000 Koln 41, West Germany |
| 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 asOln(lnL)] for the isotropic model in three dimensions where sites that fail to have at least four neighbors are culled.Related systems have been studied in the context of cellular automata.(4) |
| Keywords: | Bootstrap percolation critical exponents phase transition finite-size scaling simulation |
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