De Menech Mario
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Aug;70(2 Pt 2):028101. doi: 10.1103/PhysRevE.70.028101. Epub 2004 Aug 13.
The characterization of most of the scaling properties in sandpile models relies on numerical simulations, which allow us to collect a large number of avalanche events; in lack of an accepted theoretical framework, the estimate of the properties of probability distributions for an infinite system is based on empirical methods. Within the finite-size scaling hypothesis, for example, the scaling of the total energy dissipation s with the area a covered by the avalanche should follow the simple law s approximately a (gamma(sa) ), with gamma(sa) marking the universality class of the model; gamma(sa) is normally measured from the scaling of the average value of s given a. Chessa et al. [Phys. Rev. E 59, 12 (1999)] introduced a new procedure to extrapolate gamma(sa) for the Bak-Tang-Wiesenfeld model [P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. A 38, 364 (1988)], which leads to a value that matches the analogous exponent obtained for the Manna sandpile [S.S. Manna, J. Phys. A 24, L363 (1991)], in support of the hypothesis of a unique universality class for the two models. This procedure is discussed in detail here; it is shown how the correction used by Chessa et al. depends on the lattice size L and disappears as L--> infinity.