Disorder-induced phase transition in a one-dimensional model of rice pile

TL;DR

This paper introduces a one-dimensional rice-pile model that interpolates between two known models, revealing a sharp phase transition from trivial to self-organized critical behavior with a specific avalanche exponent.

Contribution

The study presents a novel 1D rice-pile model connecting two existing models and identifies a phase transition between different critical behaviors.

Findings

Sharp transition between trivial and SOC behavior

Model belongs to a known universality class with avalanche exponent 1.53

Transition occurs for sufficiently large system sizes

Abstract

We propose a one-dimensional rice-pile model which connects the 1D BTW sandpile model (Phys. Rev. A 38, 364 (1988)) and the Oslo rice-pile model (Phys. Rev. lett. 77, 107 (1997)) in a continuous manner. We found that for a sufficiently large system, there is a sharp transition between the trivial critical behaviour of the 1D BTW model and the self-organized critical (SOC) behaviour. When there is SOC, the model belongs to a known universality class with the avalanche exponent $\tau=1.53$.