An infinite number of effectively infinite clusters in critical percolation

Naeem Jan, Dietrich Stauffer, Amnon Aharony

Research output: Contribution to journalArticlepeer-review

Abstract

An infinite number of effectively infinite clusters are predicted at the percolation threshold, if "effectively infinite" means that a cluster's mass increases with a positive power of the lattice size L. All these cluster masses increase as LD with the fractal dimension D = d - β/v, while the mass of the rth largest cluster for fixed L decreases as l/rλ, with λ = D/d in d dimensions. These predictions are confirmed by computer simulations for the square lattice, where D = 91/48 and λ = 91/96.

Original languageEnglish
Pages (from-to)325-330
Number of pages6
JournalJournal of Statistical Physics
Volume92
Issue number1-2
DOIs
StatePublished - Jul 1998

Keywords

  • Infinite clusters
  • Percolation
  • Ranking
  • Size distribution

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