S. Lubeck et Kd. Usadel, BAK-TANG-WIESENFELD SANDPILE MODEL AROUND THE UPPER CRITICAL DIMENSION, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 56(5), 1997, pp. 5138-5143
We consider the Bak-Tang-Wiesenfeld sandpile model [Phys. Rev. Lett. 5
9, 381 (1987); Phys. Rev. A 38, 364 (1988)] on square lattices in diff
erent dimensions (D less than or equal to 6). A finite-size scaling an
alysis of the avalanche probability distributions yields the values of
the distribution exponents, the dynamical exponent. and the dimension
of the avalanches. Above the upper critical dimension D-u=4 the expon
ents equal the known mean-field values. An analysis of the area probab
ility distributions indicates that the avalanches are fractal above th
e critical dimension.