Large-scale simulations of the Zhang sandpile model

We consider the non-Abelian sandpile model introduced by Y.-C. Zhang [Phys. Rev. Lett. 63, 470 (1989)] on a two-dimensional square lattice. The static and dynamical properties of the model are investigated and compared to the Abelian sandpile model of Bak, Tang, and Wiesenfeld [Phys, Rev. Lett. 59, 381 (1987); Phys. Rev. A 38. 364 (1988)]. A detailed analysis that takes the finite-size effects into account yields that the exponents of the avalanche probability distribution are the same as in the Abelian model.