Two-component abelian sandpile models

Details Two-component abelian sandpile models Two-component abelian sandpile models

2008-10-22

arxiv.org/abs/0810.4053v2

Phys. Rev. E 79, 042102 (2009)

Physics

Condensed Matter

Statistical Mechanics

Final version. To appear in Phys.Rev.E

Scientific paper

10.1103/PhysRevE.79.042102

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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