Critical Percolation in Finite Geometries

Details Critical Percolation in Finite Geometries Critical Percolation in Finite Geometries

1991-11-14

arxiv.org/abs/hep-th/9111026v1

J.Phys. A25 (1992) L201-L206

Physics

High Energy Physics

High Energy Physics - Theory

10 pages

Scientific paper

10.1088/0305-4470/25/4/009

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.

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