A deterministic sandpile automaton revisited

TL;DR

This paper revisits a deterministic version of the BTW sandpile model, analyzing its static properties and universality class, revealing that symmetry considerations influence its critical behavior.

Contribution

It provides a detailed analysis of a deterministic BTW sandpile model, highlighting how initial conditions and boundary geometry affect its universality class.

Findings

Deterministic model's universality class depends on symmetry.

Full lattice symmetry influences critical behavior.

Numerical evidence supports boundary and initial condition effects.

Abstract

The Bak-Tang-Wiesenfeld (BTW) sandpile model is a cellular automaton which has been intensively studied during the last years as a paradigm for self-organized criticality. In this paper, we reconsider a deterministic version of the BTW model introduced by Wiesenfeld, Theiler and McNamara, where sand grains are added always to one fixed site on the square lattice. Using the Abelian sandpile formalism we discuss the static properties of the system. We present numerical evidence that the deterministic model is only in the BTW universality class if the initial conditions and the geometric form of the boundaries do not respect the full symmetry of the square lattice.