Structure of two-dimensional sandpile. I. Height probabilities |
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| Authors: | V. B. Priezzhev |
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| Affiliation: | (1) Laboratory of theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia |
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| Abstract: | The height probabilities of the two-dimensional Abelian sandpile model are the fractionial numbers of lattice sites having heights 1, 2, 3, 4. A combinatorial method for evaluation of these quantities is proposed. The method is based on mapping the set of allowed sandpile configurations onto the set of spanning trees covering a given lattice. Exact analytical expressions for all probabilities are obtained. |
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| Keywords: | Self-organized criticality sandpiles spanning trees height probabilities |
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