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Finite-Size Left-Passage Probability in Percolation

Published inJournal of Statistical Physics, vol. 149, no. 1, p. 10-36
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  • Open Access - Licence nationale Springer 
Publication date2012
Abstract

We obtain an exact finite-size expression for the probability that a percolation hull will touch the boundary, on a strip of finite width. In terms of clusters, this corresponds to the one-arm probability. Our calculation is based on the q-deformed Knizhnik–Zamolodchikov approach, and the results are expressed in terms of symplectic characters. In the large size limit, we recover the scaling behaviour predicted by Schramm's left-passage formula. We also derive a general relation between the left-passage probability in the Fortuin–Kasteleyn cluster model and the magnetisation profile in the open XXZ chain with diagonal, complex boundary terms.

Citation (ISO format)
IKHLEF, Yacine, PONSAING, Anita Kristine. Finite-Size Left-Passage Probability in Percolation. In: Journal of Statistical Physics, 2012, vol. 149, n° 1, p. 10–36. doi: 10.1007/s10955-012-0573-z
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ISSN of the journal0022-4715
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