  Due to intermittency and conservation, the Abelian sandpile in 2D obeys
multifractal, rather than finite size scaling. In the thermodynamic limit, a
vanishingly small fraction of large avalanches dominates the statistics and a
constant gap scaling is recovered in higher 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.

Statistical Mechanics