Path-crossing exponents and the external perimeter in 2D percolation

Michael Aizenman, Bertrand Aizenman, Amnon Aharony

Research output: Contribution to journalArticlepeer-review

81 Scopus citations


2D Percolation path exponents xPl describe probabilities for traversals of annuli by l non-overlapping paths, each on either occupied or vacant clusters, with at least one of each type. We relate the probabilities rigorously to amplitudes of O(N=1) models whose exponents, believed to be exact, yield xPl=(l2−1)/12. This extends to half-integers the Saleur--Duplantier exponents for k=l/2 clusters, yields the exact fractal dimension of the external cluster perimeter, DEP=2-xP3=4/3, and also explains the absence of narrow gate fjords, as originally found by Grossman and Aharony.

Original languageEnglish
Pages (from-to)1359-1362
Number of pages4
JournalPhysical Review Letters
Issue number7
StatePublished - 1 Jan 1999
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy


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