The Bak-Tang-Wiesenfeld sandpile model around the upper critical dimension
S. Lubeck, K. D. Usadel
Abstract
We consider the Bak-Tang-Wiesenfeld sandpile model 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 Du=4 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.
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