Percolation crossing formulae and conformal field theory

Jacob J H Simmons, Peter Kleban, Robert M Ziff
2007 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 the
more » ... vative of one primary operator with another. We present operator identities that support this idea and suggest the presence of additional symmetry in c=0 conformal field theories.
doi:10.1088/1751-8113/40/31/f03 fatcat:jmpgb3dyajc4rltpc3csfxy4e4