Universality Class of One-Dimensional Directed Sandpile Models

TL;DR

This paper introduces a general n-state directed sandpile model, demonstrating its universal behavior aligns with the totally asymmetric Oslo model and identifying a crossover to uncorrelated branching processes at small sizes.

Contribution

It presents a comprehensive n-state model and analytically shows its universality class, expanding understanding of one-dimensional directed sandpile models.

Findings

Model belongs to the universality class of the Oslo model

Crossover to uncorrelated branching process at small sizes

Analytical derivation of stationary properties for n<infinity

Abstract

A general n-state directed `sandpile' model is introduced. The stationary properties of the n-state model are derived for n < infty, and analytical arguments based on a central limit theorem show that the model belongs to the universality class of the totally asymmetric Oslo model, with a crossover to uncorrelated branching process behavior for small system sizes. Hence, the central limit theorem allows us to identify the existence of a large universality class of one-dimensional directed sandpile models.