Critical exponents in stochastic sandpile models

We present large scale simulations of a stochastic sandpile model in two dimensions. We use moments analysis to evaluate critical exponents and finite size scaling method to consistently test the obtained results. The general picture resulting from our analysis allows us to characterize the large scale behavior of the present model with great accuracy. Sandpile automata [1] are prototypical models to describe avalanche transport processes. All these models show a stationary state that after a suitable tuning of the driving fields[2] displays a singular response function characterized by power law distributed events. These distributions are typically bounded by upper cut-offs related to the system size. In analogy with critical phenomena, is possible to define a complete set of scaling exponents describing the large scale behavior of these models. Despite the large conceptual impact and the huge effort devoted to the study of sandpile automata in the last ten years, many basic issues, such as the precise values of the critical exponents, the identification of universality classes and of the upper critical dimension, still lay unresolved. Theoretically, many approaches [3, 4, 5] point out that different sandpile models, such as the Bak, Tang and Wiesenfeld (BTW) [1] and the Manna [6] models, all belong to the same universality class. Theoretical estimates for critical exponents have been provided (especially in Euclidean dimension d = 2) by means of different methods [3, 4, 7], and some exact results [8] can be derived from the Abelian structure of the BTW model. Numerical results