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.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)