The Oslo model, hyperuniformity, and the quenched Edwards-Wilkinson model

TL;DR

This paper investigates the 1D Oslo rice pile model, demonstrating hyperuniformity and critical exponents consistent with simple rational values, and explores its relation to the quenched Edwards-Wilkinson model.

Contribution

The study provides large-scale simulations of the Oslo model, clarifies its critical exponents, and links hyperuniformity to the correlation length exponent, also relating it to the qEW model.

Findings

Critical exponents are rational: ν=4/3, D=9/4, z=10/7.

The model exhibits hyperuniformity in the stationary state.

The local roughness exponent in the qEW model is α_loc=1.

Abstract

We present simulations of the 1-dimensional Oslo rice pile model in which the critical height at each site is randomly reset after each toppling. We use the fact that the stationary state of this sandpile model is hyperuniform to reach system of sizes $> 10^7$. Most previous simulations were seriously flawed by important finite size corrections. We find that all critical exponents have values consistent with simple rationals: $\nu=4/3$ for the correlation length exponent, $D =9/4$ for the fractal dimension of avalanche clusters, and $z=10/7 $ for the dynamical exponent. In addition we relate the hyperuniformity exponent to the correlation length exponent $\nu$. Finally we discuss the relationship with the quenched Edwards-Wilkinson (qEW) model, where we find in particular that the local roughness exponent is $\alpha_{\rm loc} = 1$.