John L.Cardy
Critical Percolation in Finite Geometries
(53K, TeX)
ABSTRACT. The methods of conformal field theory are used to compute the
crossing probabilities between segments of the boundary of a
compact two-dimensional region at the percolation threshold.
These probabilities are shown to be invariant not only under
changes of scale, but also under mappings of the region which
are conformal in the interior and continuous on the boundary.
This is a larger invariance than that expected for generic
critical systems. Specific predictions are presented for
the crossing probability between opposite sides of a rectangle, and are
compared with recent numerical work. The agreement is excellent.