Correlation, crossover, and broken scaling in the Abelian Manna model

The role of correlations in self-organized critical (SOC) phenomena is investigated by studying the Abelian Manna model (AMM) in two dimensions. Local correlations of the debris left behind after avalanches are destroyed by rearranging particles on the lattice between avalanches, without changing the one-point particle density. It is found that the spatial correlations are not relevant to small avalanches, while changing the scaling of the large (system-wide) ones, yielding a crossover in the model's scaling behavior. This crossover breaks the simple scaling observed in normal SOC.