Bak-Tang-Wiesenfeld sandpile model around the upper critical dimension

We consider the Bak-Tang-Wiesenfeld sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] on square lattices in different dimensions $(D<~6).$ A finite-size scaling analysis 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 $D_u=4\mathrm{}$ the exponents equal the known mean-field values. An analysis of the area probability distributions indicates that the avalanches are fractal above the critical dimension.