The Oslo rice pile model is a quenched Edwards-Wilkinson equation

TL;DR

This paper demonstrates that the Oslo rice pile model, a paradigm of self-organized criticality, is exactly equivalent to a discrete form of the quenched Edwards-Wilkinson equation, linking SOC to interface growth with quenched disorder.

Contribution

It establishes the first exact correspondence between a SOC model and the quenched Edwards-Wilkinson equation, enabling new analytical approaches.

Findings

Exact mapping of Oslo model to qEW equation

Connection between SOC and interface growth theories

Potential for applying interface growth techniques to SOC problems

Abstract

The Oslo rice pile model is a sandpile-like paradigmatic model of ``Self-Organized Criticality'' (SOC). In this paper it is shown that the Oslo model is in fact exactly a discrete realization of the much studied quenched Edwards-Wilkinson equation (qEW) [Nattermann et al., J. Phys. II France 2, 1483 (1992)]. This is possible by choosing the correct dynamical variable and identifying its equation of motion. It establishes for the first time an exact link between SOC models and the field of interface growth with quenched disorder. This connection is obviously very encouraging as it suggests that established theoretical techniques can be brought to bear with full strength on some of the hitherto elusive problems of SOC.