Organized versus self-organized criticality in the abelian sandpile model

Details Organized versus self-organized criticality in the abelian sandpile model Organized versus self-organized criticality in the abelian sandpile model

2005-10-17

arxiv.org/abs/math-ph/0510060v2

Markov Processes and Related Fields 2005, vol.11(3), p. 425-442

Physics

Mathematical Physics

17 pages, appeared in Markov Processes and Related Fields 2005

Scientific paper

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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