A crossing probability for critical percolation in two dimensions
Gerard Watts
Abstract
Langlands et al. considered two crossing probabilities, pih and pihv, in their extensive numerical investigations of critical percolation in two dimensions. Cardy was able to find the exact form of pih 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 pihv which compares very well with the numerical results.
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