Relevance of Abelian Symmetry and Stochasticity in Directed Sandpiles

Details Relevance of Abelian Symmetry and Stochasticity in Directed Sandpiles Relevance of Abelian Symmetry and Stochasticity in Directed Sandpiles

2008-07-11

arxiv.org/abs/0807.1807v3

Phys. Rev. Lett. 101, 218001 (2008)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures; published version

Scientific paper

10.1103/PhysRevLett.101.218001

We provide a comprehensive view on the role of Abelian symmetry and stochasticity in the universality class of directed sandpile models, in context of the underlying spatial correlations of metastable patterns and scars. It is argued that the relevance of Abelian symmetry may depend on whether the dynamic rule is stochastic or deterministic, by means of the interaction of metastable patterns and avalanche flow. Based on the new scaling relations, we conjecture critical exponents for avalanche, which is confirmed reasonably well in large-scale numerical simulations.

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