2016/06/08 by Peter Grassberger, Deepak Dhar, P. K. Mohanty · 41 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Combinatorics #Complex Systems and Time Series Analysis #Condensed matter physics #Critical exponent #Dimension (graph theory) #Exponent #Fractal #Mathematical analysis #Mathematical physics #Mathematics #Phase transition #Physics #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.94.042314
published in Physical review. E 94(4), 042314 (American Physical Society) · 20 pages, 26 figures
arxiv created 2016/06/08 · openalex publication_date 2016/10/25 · arxiv updated 2016/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 >107. Most previous simulations were seriously flawed by important finite-size corrections. We find that all critical exponents have values consistent with simple rationals: ν=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 ν. Finally, we discuss the relationship with the quenched Edwards-Wilkinson model, where we find in particular that the local roughness exponent is αloc=1.