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Mean-field behavior of the sandpile model below the upper critical dimension | | Alessandro Chessa
; Enzo Marinari
; Alessandro Vespignani
; Stefano Zapperi
; | | Date: |
11 Feb 1998 | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Affiliation: | Cagliari, Italy), Enzo Marinari (Cagliari, Italy), Alessandro Vespignani (ICTP Trieste, Italy), Stefano Zapperi (Boston Univ., USA | | 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 $2leq dleq 6$. 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 $d_cgeq 5$. 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. | | Source: | arXiv, cond-mat/9802123 | | Services: | Forum | Review | PDF | Favorites | |
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