Two-component abelian sandpile models

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.

Final version. To appear in Phys.Rev.E