Infinite clusters in percolation models

C. M. Newman, L. S. Schulman

Research output: Contribution to journalArticlepeer-review


The qualitative nature of infinite clusters in percolation models is investigated. The results, which apply to both independent and correlated percolation in any dimension, concern the number and density of infinite clusters, the size of their external surface, the value of their (total) surface-to-volume ratio, and the fluctuations in their density. In particular it is shown that N0, the number of distinct infinite clusters, is either 0, 1, or ∞ and the case N0=∞ (which might occur in sufficiently high dimension) is analyzed.

Original languageEnglish (US)
Pages (from-to)613-628
Number of pages16
JournalJournal of Statistical Physics
Issue number3
StatePublished - Nov 1981


  • Percolation
  • cluster density
  • infinite clusters
  • surface-to-volume ratio

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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