Organized Versus Self-Organized Criticality in the Abelian Sandpile Model

A. Fey-den Boer, F. Redig

2005, v.11, Issue 3, 425-442

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.

Keywords: self-organized criticality,Abelian sandpile model,activatedrandom walkers,stabilizability