Finite-Size Effects for Some Bootstrap Percolation Models

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

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    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 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.
    Original languageEnglish
    Pages (from-to)323-332
    Number of pages10
    JournalJournal of Statistical Physics
    Volume60
    Issue number3-4
    DOIs
    Publication statusPublished - Aug-1990

    Keywords

    • simulation
    • finite-size scaling
    • phase transition
    • critical exponents
    • bootstrap percolation

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