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arXiv · 1511.06088

Directed Abelian sandpile with multiple downward neighbors

Deepak Dhar·Gunnar Pruessner·Paul Expert·Kim Christensen·Nicky Zachariou
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Abstract

We study the directed Abelian sandpile model on a square lattice, with $K$ downward neighbors per site, $K > 2$. The $K=3$ case is solved exactly, which extends the earlier known solution for the $K=2$ case. For $K>2$, the avalanche clusters can have holes and side-branches and are thus qualitatively different from the $K=2$ case where avalance clusters are compact. However, we find that the critical exponents for $K>2$ are identical with those for the $K=2$ case, and the large scale structure of the avalanches for $K>2$ tends to the $K=2$ case.

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Deepak Dhar, Gunnar Pruessner, Paul Expert, Kim Christensen, Nicky Zachariou. 2016-02-11. Directed Abelian sandpile with multiple downward neighbors. https://doi.org/10.1103/physreve.93.042107

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