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Organized versus self-organized criticality in the abelian sandpile model

A. Fey·F. Redig
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Abstract

We define stabilizability of an infinite volume height configuration and of a probability measure on height configurations. We show that for high enough densities, a probability measure cannot be stabilized. We also show that in some sense the thermodynamic limit of the uniform measures on the recurrent configurations of the abelian sandpile model (ASM) is a maximal element of the set of stabilizable measures. In that sense the self-organized critical behavior of the ASM can be understood in terms of an ordinary transition between stabilizable and non-stabilizable

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A. Fey, F. Redig. 2005-11-17. Organized versus self-organized criticality in the abelian sandpile model. https://arxiv.org/abs/math-ph/0510060

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