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

Abstract

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 $2\le d\le 6$. 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 $d_c\ge 5$. 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.

4 RevTex pages, 2 eps figures embedded

References in corpus (5)

• Universality in Sandpile Models
• Order Parameter and Scaling Fields in Self-Organized Criticality
• Numerical Determination of the Avalanche Exponents of the Bak-Tang-Wiesenfeld Model
• Large scale simulations of the Zhang sandpile model
• The Bak-Tang-Wiesenfeld sandpile model around the upper critical dimension

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• Fluctuations and correlations in sandpile models
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• Non conservative Abelian sandpile model with BTW toppling rule
• Kinetic description of avalanching systems