Large scale simulations of the Zhang sandpile model

TL;DR

This paper investigates the Zhang non-Abelian sandpile model through large-scale simulations, analyzing its static and dynamic properties and comparing them to the well-known Abelian model, revealing similar avalanche exponents.

Contribution

It provides the first detailed finite-size analysis of the Zhang model, showing that its avalanche distribution exponents match those of the Abelian model.

Findings

Avalanche exponents are identical to the Abelian model

Finite size effects are significant in the analysis

Static and dynamic properties are thoroughly characterized

Abstract

We consider the non Abelian sandpile model introduced by Y.-C. Zhang on a two-dimensional square lattice. The static and dynamical properties of the model are investigated and compared to the Abelian sandpile model of Bak, Tang and Wiesenfeld. A detailed analysis which takes the finite size effects into account yields that the exponents of the avalanche probability distribution are the same as in the Abelian model.