On the universality of crossing probabilities in two-dimensional percolation |
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| Authors: | R P Langlands C Pichet Ph Pouliot Y Saint-Aubin |
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| Institution: | (1) Institute for Advanced Study, 08540 Princeton, New Jersey;(2) Département de mathématiques et d'informatique, UQAM, H3C 3P8 Montréal, Canada;(3) Département de mathématiques et de statistique et Département de physique, Université de Montréal, H3C 3J7 Montréal, Canada;(4) Centre de recherches mathématiques et Département de mathématiques et de statistique, Université de Montréal, H3C 3J7 Montréal, Canada |
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| Abstract: | Six percolation models in two dimensions are studied: percolation by sites and by bonds on square, hexagonal, and triangular lattices. Rectangles of widtha and heightb are superimposed on the lattices and four functions, representing the probabilities of certain crossings from one interval to another on the sides, are measured numerically as functions of the ratioa/b. In the limits set by the sample size and by the conventions and on the range of the ratioa/b measured, the four functions coincide for the six models. We conclude that the values of the four functions can be used as coordinates of the renormalization-group fixed point. |
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| Keywords: | Percolation in two dimensions universality classes in percolation theory renormalization group |
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