Corrections to scaling and probability distribution of avalanches for the stochastic Zhang sandpile model

We study the distributions of dissipative and nondissipative avalanches separately in the stochastic Zhang (SP-Z) sandpile in two dimension. We find that dissipative and nondissipative avalanches obey simple power laws and do not have the logarithmic correction, while the avalanche distributions in the Abelian Manna model should include a logarithmic correction. We use the moment analysis to determine the numerical critical exponents of dissipative and nondissipative avalanches, respectively, and find that they are different from the corresponding values in the Abelian Manna model. All these indicate that the stochastic Zhang model and the Abelian Manna model belong to distinct universality classes, which imply that the Abelian symmetry breaking changes the scaling behavior of the avalanches in the case of the stochastic sandpile model.