Universality classes in isotropic, Abelian, and non-Abelian sandpile models

Universality in isotropic, Abelian, and non-Abelian, sandpile models is examined using extensive numerical simulations. To characterize the critical behavior we employ an extended set of critical exponents, geometric features of the avalanches, as well as scaling functions describing the time evolution of average quantities such as the area and size during the avalanche. Comparing between the Abelian Bak-Tang-Wiesenfeld model [P. Bak, C. Tang, and K. Wiensenfeld, Phys. Rev. Lett. 59, 381 (1987)] and the non-Abelian models introduced by Manna [S. S. Manna, J. Phys. A 24, L363 (1991)] and Zhang [Y. C. Zhang, Phys. Rev. Lett. 63, 470 (1989)] we find strong indications that each one of these models belongs to a distinct universality class.