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

TL;DR

This paper investigates the Abelian Manna model's critical behavior across various lattices, confirming universality below the upper critical dimension and deriving an xpansion with a notable relation involving lattice and random walker dimensions.

Contribution

The study provides high-accuracy critical exponents for the Abelian Manna model on diverse lattices and establishes an xpansion framework incorporating fractal and regular lattices.

Findings

Critical exponents are consistent across different lattice types.

A universal relation involving lattice and random walker dimensions is identified.

An xpansion for the model's critical behavior is derived.

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.