Finite-Size Left-Passage Probability in Percolation |
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Authors: | Yacine Ikhlef Anita K Ponsaing |
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Institution: | 1.Section de Mathématiques,University of Geneva,Geneva,Switzerland |
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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. |
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