title: 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 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.
authors.affiliation: Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400005, India.
authors.forename: D
authors.initials: D
authors.lastname: Dhar
authors.affiliation: Department of Mathematics, Imperial College London, London, South Kensington Campus, London SW7 2AZ, United Kingdom.|Centre for Complexity Science, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom.
authors.forename: G
authors.initials: G
authors.lastname: Pruessner
authors.affiliation: Centre for Complexity Science, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom.|Department of Physics, Blackett Laboratory, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom.|Centre for Neuroimaging Sciences, Institute of Psychiatry, King's College London, London SE5 8AF, United Kingdom.
authors.forename: P
authors.initials: P
authors.lastname: Expert
authors.affiliation: Centre for Complexity Science, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom.|Department of Physics, Blackett Laboratory, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom.
authors.forename: K
authors.initials: K
authors.lastname: Christensen
authors.affiliation: Centre for Complexity Science, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom.|Department of Physics, Blackett Laboratory, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom.
authors.forename: N
authors.initials: N
authors.lastname: Zachariou