Directed Abelian sandpile with multiple downward neighbors.
basic_science · Level V
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- Record sourced from PubMed, PMID 27176254.
- Also identified by DOI 10.1103/PhysRevE.93.042107.
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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 avalanche 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.