Numerical results for crossing, spanning and wrapping in two-dimensional percolation

Details Numerical results for crossing, spanning and wrapping in two-dimensional percolation Numerical results for crossing, spanning and wrapping in two-dimensional percolation

2003-09-05

arxiv.org/abs/cond-mat/0309126v1

J. Phys. A: Math. Gen. 36, 11213-11228 (2003)

Physics

Condensed Matter

Statistical Mechanics

19 pages, 9 figures, JPA style, accepted for publication

Scientific paper

10.1088/0305-4470/36/44/003

Using a recently developed method to simulate percolation on large clusters of distributed machines [N. R. Moloney and G. Pruessner, Phys. Rev. E 67, 037701 (2003)], we have numerically calculated crossing, spanning and wrapping probabilities in two-dimensional site and bond percolation with exceptional accuracy. Our results are fully consistent with predictions from Conformal Field Theory. We present many new results that await theoretical explanation, particularly for wrapping clusters on a cylinder. We therefore provide possibly the most up-to-date reference for theoreticians working on crossing, spanning and wrapping probabilities in two-dimensional percolation.

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