Confirming and extending the hypothesis of universality in sandpiles

TL;DR

This paper confirms that a previously debated sandpile automaton belongs to the C-DP universality class, supporting the universality hypothesis for stochastic sandpiles through simulations and field theory analysis.

Contribution

It demonstrates that the Maslov-Zhang sandpile automaton is in the C-DP class, resolving a long-standing debate and strengthening the universality principle in self-organized criticality.

Findings

The Maslov-Zhang automaton belongs to the C-DP class.

A new method to distinguish DP from C-DP scaling.

Numerical and theoretical evidence supporting universality.

Abstract

Stochastic sandpiles self-organize to a critical point with scaling behavior different from directed percolation (DP) and characterized by the presence of an additional conservation law. This is usually called C-DP or Manna universality class. There remains, however, an exception to this universality principle: a sandpile automaton introduced by Maslov and Zhang, which was claimed to be in the directed percolation class despite of the existence of a conservation law. In this paper we show, by means of careful numerical simulations as well as by constructing and analyzing a field theory, that (contrarily to what previously thought) this sandpile is also in the C-DP or Manna class. This confirms the hypothesis of universality for stochastic sandpiles, and gives rise to a fully coherent picture of self-organized criticality in systems with a conservation law. In passing, we obtain a number of results for the C-DP class and introduce a new strategy to easily discriminate between DP and C-DP scaling.