Directed Abelian sandpile with multiple downward neighbors

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.

Accepted for publication in PRE

References in corpus (4)

• Theoretical Results for Sandpile Models of SOC with Multiple Topplings
• On the scaling of probability density functions with apparent power-law exponents less than unity
• Logarithmic corrections of the avalanche distributions of sandpile models at the upper critical dimension
• Fragmentation of a sheet by propagating, branching and merging cracks