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

Abstract

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.

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

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• Winding clusters in percolation on the Torus and the Moebius strip
• Dulmage-Mendelsohn percolation: Geometry of maximally-packed dimer models and topologically-protected zero modes on site-diluted bipartite lattices
• Alternative criterion for two-dimensional wrapping percolation
• Critical p=1/2 in percolation on semi-infinite strips
• Percolation crossing probabilities in hexagons: a numerical study
• Continuum Percolation on Disoriented Surfaces: the Problem of Permeable Disks on a Klein Bottle