Evidence for universality within the classes of deterministic and stochastic sandpile models - art. no. 061309

Recent numerical studies have provided evidence that within the family of c onservative, undirected sandpile models with short range dynamic rules, det erministic models such as the Bak-Tang-Wiesenfeld model [P. Bak, C. Tang, a nd K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)] and stochastic models su ch as the Manna model [S. S. Manna, J. Phys. A 24, L363 (1991)] belong to d ifferent universality classes. In this paper we examine the universality wi thin each of the two classes in two dimensions by numerical simulations. To this end we consider additional deterministic and stochastic models and us e an extended set of critical exponents, scaling functions, and geometrical features. Universal behavior is found within the class of deterministic Ab elian models, as well as within the class of stochastic models (which inclu des both Abelian and non-Abelian models). In addition, it is observed that deterministic but non-Abelian models exhibit critical exponents that depend on a parameter, namely they are nonuniversal.