title: Abelian Manna model in three dimensions and below.
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 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.
authors.affiliation: Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore. n.huynh10@imperial.ac.uk
authors.forename: Hoai Nguyen
authors.initials: HN
authors.lastname: Huynh
authors.forename: Gunnar
authors.initials: G
authors.lastname: Pruessner
mesh_terms: D003102:Colloids / Q000737:chemistry*; D003198:Computer Simulation; D003460:Crystallization / Q000379:methods*; D008956:Models, Chemical; D015233:Models, Statistical
chemical_list: D003102:Colloids