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

We present simulations of the one-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 sand-pile 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.. Finally, we discuss the relationship with the quenched Edwards-Wilkinson model, where we find in particular that the local roughness exponent is alpha(loc) = 1.