Abelian Manna model on various lattices in one and two dimensions

Abstract

We perform a high-accuracy moment analysis of the avalanche size, duration and area distribution of the Abelian Manna model on eight two-dimensional and four one-dimensional lattices. The results provide strong support to establish universality of exponents and moment ratios across different lattices and a good survey for the strength of corrections to scaling which are notorious in the Manna universality class. The results are compared against previous work done on Manna model, Oslo model and directed percolation. We also confirm hypothesis of various scaling relations.

16 pages, 3 figures, 7 tables, submitted to Journal of Statistical Mechanics

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• Coupling of $c=-2$ and $c=\frac{1}{2}$ and $c=0$ conformal field theories: The geometrical point of view
• Dissipative stochastic sandpile model on small world network : properties of non-dissipative and dissipative avalanches
• Crossover from rotational to stochastic sandpile universality in the random rotational sandpile model
• Anchored advected interfaces, Oslo model, and roughness at depinning
• Conservative self-organized extremal model for wealth distribution
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• Critical properties of deterministic and stochastic sandpile models on two-dimensional percolation backbone
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• The average avalanche size in the Manna Model and other models of self-organised criticality
• Critical Density of the Abelian Manna Model via a Multi-type Branching Process