Abelian Manna model on various lattices in one and two dimensions

TL;DR

This study conducts a detailed analysis of the Abelian Manna model across multiple lattice types in one and two dimensions, confirming universality of critical exponents and scaling relations, and highlighting correction-to-scaling effects.

Contribution

It provides high-accuracy moment analysis across various lattices, supporting universality and comparing results with related models and theories.

Findings

Universality of exponents and moment ratios across different lattices

Strong corrections to scaling observed in the Manna universality class

Confirmation of various scaling relations

Abstract

We perform a high-accuracy moment analysis of the avalanche size, duration and area distribution of the Abelian Manna model on eight two-dimensional and four one-dimensional lattices. The results provide strong support to establish universality of exponents and moment ratios across different lattices and a good survey for the strength of corrections to scaling which are notorious in the Manna universality class. The results are compared against previous work done on Manna model, Oslo model and directed percolation. We also confirm hypothesis of various scaling relations.