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On Cardy's formula for the critical crossing probability in 2D percolation

Ziff, Robert M.

Ziff, Robert M.

1995-03-07

Citation:Ziff, R M (1995). "On Cardy's formula for the critical crossing probability in 2D percolation." Journal of Physics A: Mathematical and General. 28(5): 1249-1255. <http://hdl.handle.net/2027.42/48834>

Abstract: Cardy's formula for the probability pi nu (r) of crossing a rectangular critical percolation system in the vertical direction, with free boundaries on the two sides, is written explicitly in terms of the aspect ratio r=height/width. The first three terms are given by pi nu (r)=243/3 Gamma (2/3)/ Gamma (1/3)2(e- pi r3/-4/7e-7 pi 3/+2/13e-13 pi r3/...) which, with pi nu (r)=1- pi nu (1/r), are sufficient to determine pi nu (r) to high accuracy for all r.