We present results of large scale numerical simulations of the Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] sandpile model. We analyze the critical behavior of the model in Euclidean dimensions [formula presented]. 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 [formula presented] significantly differ from mean-field predictions, thus suggesting an upper critical dimension [formula presented]. Using the relations among the dissipation rate [formula presented] and the finite lattice size [formula presented], 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.
Mean-field behavior of the sandpile model below the upper critical dimension / A. Chessa, E. Marinari, A. Vespignani, S. Zapperi. - In: PHYSICAL REVIEW E. - ISSN 1063-651X. - 57:6(1998 Jun 01), pp. R6241-R6244.
Mean-field behavior of the sandpile model below the upper critical dimension
S. Zapperi
1998
Abstract
We present results of large scale numerical simulations of the Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] sandpile model. We analyze the critical behavior of the model in Euclidean dimensions [formula presented]. 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 [formula presented] significantly differ from mean-field predictions, thus suggesting an upper critical dimension [formula presented]. Using the relations among the dissipation rate [formula presented] and the finite lattice size [formula presented], 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.File | Dimensione | Formato | |
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