Abelian Manna model in three dimensions and below.
Huynh, Hoai Nguyen.
Date of Issue2012
School of Physical and Mathematical Sciences
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 coefficients of an ε expansion. By 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.
Physical Review E
© 2012 American Physical Society. This paper was published in Physical Review E and is made available as an electronic reprint (preprint) with permission of American Physical Society. The paper can be found at the following official DOI: [http://dx.doi.org/10.1103/PhysRevE.85.061133]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.