Finite-Size Effects for Some Bootstrap Percolation Models

A. C. D. van Enter, Joan Adler, J. A. M. S. Duarte

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    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 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.
    Originele taal-2English
    Pagina's (van-tot)323-332
    Aantal pagina's10
    TijdschriftJournal of Statistical Physics
    Volume60
    Nummer van het tijdschrift3-4
    DOI's
    StatusPublished - aug-1990

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