On The Avalanche-finiteness Of Abelian Sandpiles

Details On The Avalanche-finiteness Of Abelian Sandpiles On The Avalanche-finiteness Of Abelian Sandpiles

1994-10-17

arxiv.org/abs/adap-org/9410002v1

Physics

Condensed Matter

8 pages with no figure, typeset using RevTex 3.0 with some symbols from AMS Fonts as well

Scientific paper

We prove a necessary and sufficient condition for an Abelian Sandpile Model (ASM) to be avalanche-finite, namely: all unstable states of the system can be brought back to stability in finite number of topplings. The method is also computationally feasible since it involves no greater than $\mbox{O} \left( N^3 \right)$ arithmetic computations where $N$ is the total number of sites of the system. Key words: Abelian sandpile model; avalanche-finiteness; self-organized criticality

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