Scientific article
Open access

Finite-Size Left-Passage Probability in Percolation

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

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
Main files (1)
Article (Published version)
ISSN of the journal0022-4715

Technical informations

Creation03/11/2019 2:27:00 PM
First validation03/11/2019 2:27:00 PM
Update time03/15/2023 3:50:47 PM
Status update03/15/2023 3:50:47 PM
Last indexation01/17/2024 5:05:20 AM
All rights reserved by Archive ouverte UNIGE and the University of GenevaunigeBlack