Abelian Manna model in three dimensions and below

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 epsilon 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.