Directed Abelian sandpile with multiple downward neighbors

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Directed Abelian sandpile with multiple downward neighbors

D. Dhar, G. Pruessner, P. Expert, K. Christensen, and N. Zachariou

Phys. Rev. E 93, 042107 – Published 8 April 2016

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.

Received 23 November 2015

DOI:https://doi.org/10.1103/PhysRevE.93.042107

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Published by the American Physical Society

Physics Subject Headings (PhySH)

Sandpile models

Statistical Physics & Thermodynamics

Authors & Affiliations

D. Dhar^1,*, G. Pruessner^2,3,†, P. Expert^3,4,5,‡, K. Christensen^3,4,§, and N. Zachariou^3,4,∥

¹Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400005, India
²Department of Mathematics, Imperial College London, London, South Kensington Campus, London SW7 2AZ, United Kingdom
³Centre for Complexity Science, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
⁴Department of Physics, Blackett Laboratory, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
⁵Centre for Neuroimaging Sciences, Institute of Psychiatry, King's College London, London SE5 8AF, United Kingdom

^*Electronic address: ddhar@theory.tifr.res.in
^†Electronic address: g.pruessner@imperial.ac.uk
^‡Electronic address: paul.expert@kcl.ac.uk
^§Electronic address: k.christensen@imperial.ac.uk
^∥Electronic address: nicky.zachariou@imperial.ac.uk

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Issue

Vol. 93, Iss. 4 — April 2016

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