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Percolation crossing formulae and conformal field theory
Journal of Physics A: Mathematical and Theoretical
Using conformal field theory, we derive several new crossing formulas at the two-dimensional percolation point. High-precision simulation confirms these results. Integrating them gives a unified derivation of Cardy's formula for the horizontal crossing probability Π_h(r), Watts' formula for the horizontal-vertical crossing probability Π_hv(r), and Cardy's formula for the expected number of clusters crossing horizontally N_h(r). The main step in our approach implies the identification of thedoi:10.1088/1751-8113/40/31/f03 fatcat:jmpgb3dyajc4rltpc3csfxy4e4