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
Publication statusPublished - Aug-1990

Keywords

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

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