Correlations and hyperuniformity in the avalanche size of the Oslo Model

Abstract: Certain random processes display anticorrelations resulting in local Poisson-like disorder and global order, where correlations suppress fluctuations. Such processes are called hyperuniform. Using a map to an interface picture we show via analytic calculations that a sequence of avalanche sizes of the Oslo Model is hyperuniform in the temporal domain with the minimal exponent $\lambda=0$. We identify the conserved quantity in the interface picture that gives rise to the hyperuniformity in the avalanche size. We further discuss the fluctuations of the avalanche size in two variants of the Oslo Model. We support our findings with numerical results.