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arXiv · 0810.4053

Two-component abelian sandpile models

F. C. Alcaraz·P. Pyatov·V. Rittenberg
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Abstract

In one-component abelian sandpile models, the toppling probabilities are independent quantities. This is not the case in multi-component models. The condition of associativity of the underlying abelian algebras impose nonlinear relations among the toppling probabilities. These relations are derived for the case of two-component quadratic abelian algebras. We show that abelian sandpile models with two conservation laws have only trivial avalanches.

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F. C. Alcaraz, P. Pyatov, V. Rittenberg. 2009-03-12. Two-component abelian sandpile models. https://doi.org/10.1103/physreve.79.042102

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