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

Chessa, Alessandro and Marinari, Enzo and Vespignani, Alessandro and Zapperi, Stefano Mean-field behavior of the sandpile model below the upper critical dimension. Physical Review E, 57. R6241-R6244. ISSN 1539-3755 (1998)

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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<~d<~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 dc>~5. Using the relations among the dissipation rate ε 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.

Item Type: Article
Identification Number: 10.1103/PhysRevE.57.R6241
Uncontrolled Keywords: PACS: 64.60.Lx, 05.40.+j, 05.70.Ln
Subjects: Q Science > QC Physics
Research Area: Economics and Institutional Change
Depositing User: Ms T. Iannizzi
Date Deposited: 06 Nov 2013 11:00
Last Modified: 20 Nov 2013 08:53
URI: http://eprints.imtlucca.it/id/eprint/1871

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