Journal of Statistical Physics

, Volume 60, Issue 3–4, pp 323–332 | Cite as

Finite-size effects for some bootstrap percolation models

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


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.

Key words

Bootstrap percolation critical exponents phase transition finite-size scaling simulation 


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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • A. C. D. van Enter
    • 1
  • Joan Adler
    • 2
    • 3
  • J. A. M. S. Duarte
    • 4
    • 5
  1. 1.Institute of Theoretical PhysicsRUGGroningenThe Netherlands
  2. 2.Department of PhysicsTechnionHaifaIsrael
  3. 3.Department of Physics and AstronomyUniversity of Tel AvivRamat AvivIsrael
  4. 4.HLRZJülich
  5. 5.Institut für Theoretische PhysikKoln 41West Germany

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