TY - JOUR
T1 - Path-crossing exponents and the external perimeter in 2D percolation
AU - Aizenman, Michael
AU - Aizenman, Bertrand
AU - Aharony, Amnon
PY - 1999/1/1
Y1 - 1999/1/1
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevLett.83.1359
DO - 10.1103/PhysRevLett.83.1359
M3 - Article
AN - SCOPUS:0000360856
SN - 0031-9007
VL - 83
SP - 1359
EP - 1362
JO - Physical review letters
JF - Physical review letters
IS - 7
ER -