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

S. Lubeck·K. D. Usadel
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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 D_u=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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S. Lubeck, K. D. Usadel. 1997-08-07. The Bak-Tang-Wiesenfeld sandpile model around the upper critical dimension. https://doi.org/10.1103/physreve.56.5138

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