 992 Michael Aizenman, Bertrand Duplantier, Amnon Aharony
 Path Crossing Exponents and the External Perimeter
in 2D Percolation
(123K, Latex, 4 pages, 2 figures (epsf))
Jan 4, 99

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Abstract. Percolation path crossing exponents describe probabilities
for $\ell$ nonoverlapping traversing paths, each of either
occupied sites or vacancies. We show, for collections
including at least one of each, that in 2D the exponents
are those of an $O(N=1)$ loop model. This extends the earlier
identification by Saleur and Duplantier of $k$ spanning
cluster exponents, for which $\ell=2k$. The results yield
$D_{EP}=4/3$ for the fractal dimension of the accessible
external cluster perimeter, and explain the absence of narrow gate
fjords, in agreement with the original findings of Grossman and Aharony.
 Files:
992.src(
992.comments ,
992.keywords ,
path.jan4.tex ,
gates.eps ,
paths.eps )