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

Michael Aizenman, Bertrand Aizenman, Amnon Aharony

Research output: Contribution to journalArticlepeer-review

76 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 (US)
Pages (from-to)1359-1362
Number of pages4
JournalPhysical review letters
Issue number7
StatePublished - Jan 1 1999

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)


Dive into the research topics of 'Path-crossing exponents and the external perimeter in 2D percolation'. Together they form a unique fingerprint.

Cite this