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 2 less than or equal to d less than or equal to 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)greater than or equal to 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.

Notes

Originally published in Physical Review E, v.57 no.6 (1998), pp.R6241-R6244. DOI:10.1103/PhysRevE.57.R6241. Dr. Vespignani is affiliated with Northeastern University as of the time of deposit.

Keywords

sandpile models

Subject Categories

Mean field theory, Energy dissipation, Conservation laws (Physics)

Disciplines

Physics

Publisher

American Physical Society

Publication Date

6-1-1998

Rights Information

©1998 American Physical Society

Rights Holder

American Physical Society

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