Universality and a numerical \epsilon-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 \epsilon-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.