Winding Clusters in Percolation on the Torus and the Möbius Strip |
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Authors: | Pruessner Gunnar Moloney Nicholas R. |
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Affiliation: | 1. Department of Mathematics, Imperial College London, 180 Queen's Gate, London, SW7 2BZ, United Kingdom 2. Condensed Matter Theory, Blackett Laboratory, Imperial College London, Prince Consort Rd, London, SW7 2BW, United Kingdom
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Abstract: | Using a simulation technique introduced recently, we study winding clusters in percolation on the torus and the Möbius strip for different aspect ratios. The asynchronous parallelization of the simulation makes very large system and sample sizes possible. Our high accuracy results are fully consistent with predictions from conformal field theory. The numerical results for the Möbius strip and the number distribution of winding clusters on the torus await theoretical explanation. To our knowledge, this study is the first of its kind. |
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