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A crossing probability for critical percolation in two dimensions

Gerard Watts
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Abstract

Langlands et al. considered two crossing probabilities, pi_h and pi_{hv}, in their extensive numerical investigations of critical percolation in two dimensions. Cardy was able to find the exact form of pi_h by treating it as a correlation function of boundary operators in the Q goes to 1 limit of the Q state Potts model. We extend his results to find an analogous formula for pi_{hv} which compares very well with the numerical results.

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Gerard Watts. 1996-04-03. A crossing probability for critical percolation in two dimensions. https://doi.org/10.1088/0305-4470%2F29%2F14%2F002

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