Mean-field behavior of the sandpile model below the upper critical dimension

Details Mean-field behavior of the sandpile model below the upper critical dimension Mean-field behavior of the sandpile model below the upper critical dimension

1998-02-11

arxiv.org/abs/cond-mat/9802123v1

Physics

Condensed Matter

Statistical Mechanics

4 RevTex pages, 2 eps figures embedded

Scientific paper

10.1103/PhysRevE.57.R6241

We present results of large scale numerical simulations of the Bak, Tang and Wiesenfeld sandpile model. We analyze the critical behavior of the model in Euclidean dimensions $2\leq d\leq 6$. We consider a dissipative generalization of the model and study the avalanche size and duration distributions for different values of the lattice size and dissipation. We find that the scaling exponents in $d=4$ significantly differ from mean-field predictions, thus suggesting an upper critical dimension $d_c\geq 5$. Using the relations among the dissipation rate $\epsilon$ and the finite lattice size $L$, we find that a subset of the exponents displays mean-field values below the upper critical dimensions. This behavior is explained in terms of conservation laws.

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