Universality classes for rice-pile models

TL;DR

This paper explores sandpile models with stochastic updates and nonlocal relaxation, revealing three universality classes with distinct critical exponents and linking these to interface models.

Contribution

It identifies new universality classes for sandpile models with nonlocal relaxation, expanding understanding of critical behavior in such systems.

Findings

Models with local relaxation have avalanche exponent τ ≈ 1.55.

Models with nonlocal relaxation exhibit exponents τ ≈ 1.35 and τ ≈ 1.63.

Different relaxation rules lead to distinct universality classes.

Abstract

We investigate sandpile models where the updating of unstable columns is done according to a stochastic rule. We examine the effect of introducing nonlocal relaxation mechanisms. We find that the models self-organize into critical states that belong to three different universality classes. The models with local relaxation rules belong to a known universality class that is characterized by an avalanche exponent $\tau \approx 1.55$, whereas the models with nonlocal relaxation rules belong to new universality classes characterized by exponents $\tau \approx 1.35$ and $\tau \approx 1.63$. We discuss the values of the exponents in terms of scaling relations and a mapping of the sandpile models to interface models.