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Article

Two-component abelian sandpile models

Alcaraz F. C., Pyatov P. N., Rittenberg V.
In one-component Abelian sandpile models, the toppling probabilities are independent quantities. This is not the case in multicomponent models. The condition of associativity of the underlying Abelian algebras imposes nonlinear relations among the toppling probabilities. These relations are derived for the case of two-component сuadratic Abelian algebras.We show that Abelian sandpile models with two conservation laws have only trivial avalanches.