Density profile of the incipient infinite percolation cluster

Dietrich Stauffer*, Amnon Aharony

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Monte Carlo simulations show simple scaling for the number of sites in the spanning cluster at the percolation threshold as a function of distance from the border. The results for free boundary conditions represent crossover from surface to bulk fractal dimensions, and the former agrees with exact results in d = 2 and d = 6 - ∈ dimensions and with earlier simulations. We also present and explain results for bus-bar boundary conditions, with two types of connection rules. The scaling functions, which are predicted to be universal, surprisingly seem not to depend on the aspect ratios of the samples.

Original languageEnglish
Pages (from-to)935-940
Number of pages6
JournalInternational Journal of Modern Physics C
Issue number5
StatePublished - Jul 1999
Externally publishedYes


  • Connectivity Function
  • Critical Exponents
  • Dimensionality Dependence


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