Breakdown of self-organized criticality in sandpiles

We introduce two sandpile models which show the same behavior of real sandpiles, that is, an almost self-organized critical behavior for small systems and a dominance of large avalanches as the system size increases. The systems become fully self-organized critical, with the critical exponents of the Bak, Tank, and Wiesenfeld model [P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)] as the system parameters are changed, showing that they can make a bridge between the well known theoretical and numerical results and what is observed in real experiments.