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Percolation pp 148-168 | Cite as

Near the Critical Point: Scaling Theory

  • Geoffrey Grimmett

Abstract

The behaviour of the percolation process on L d depends dramatically on whether p < p c or p > p c . In the former subcritical case, all open clusters are almost surely finite and their size-distribution has a tail which decays exponentially. In the latter supercritical case, there exists almost surely an infinite open cluster and the size-distribution of the remaining finite open clusters has a tail which decays slower than exponentially. Some of the major differences between these two phases are highlighted in the following table.

Keywords

Correlation Length Critical Exponent Open Cluster Percolation Process Asymptotic Relation 
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Notes

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Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • Geoffrey Grimmett
    • 1
  1. 1.School of MathematicsUniversity of BristolBristolEngland

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