RARE EVENTS AND BREAKDOWN OF SIMPLE SCALING IN THE ABELIAN SANDPILE MODEL

Due to intermittency and conservation, the Abelian sandpile in two dim ensions obeys multifractal, rather than finite size scaling. In the th ermodynamic limit, a vanishingly small fraction of large avalanches do minates the statistics and a constant gap scaling is recovered in high er moments of the toppling distribution. Thus, rare events shape most of the scaling pattern and preserve a meaning for effective exponents, which can be determined on the basis of numerical and exact results.