Universality and a numerical ε-expansion of the Abelian Manna model below upper critical dimension

Abstract

The Abelian Manna model of self-organized criticality is studied on various three-dimensional and fractal lattices. The exponents for avalanche size, duration and area distribution of the model are obtained by using a high-accuracy moment analysis. Together with earlier results on lower-dimensional lattices, the present results reinforce the notion of universality below the upper critical dimension and allow us to determine the the coefficients of an ε-expansion. Rescaling the critical exponents by the lattice dimension and incorporating the random walker dimension, a remarkable relation is observed, satisfied by both regular and fractal lattices.

6 pages, 3 figures, 6 tables, submitted to PRE

References in corpus (2)

• Abelian Manna model on various lattices in one and two dimensions
• The Abelian Manna model on two fractal lattices

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• Self-organised criticality in stochastic sandpiles: Connection to directed percolation
• Critical properties of deterministic and stochastic sandpile models on two-dimensional percolation backbone
• 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