Universality Classes in Isotropic, Abelian and non-Abelian, Sandpile Models

Details Universality Classes in Isotropic, Abelian and non-Abelian, Sandpile Models Universality Classes in Isotropic, Abelian and non-Abelian, Sandpile Models

1998-03-12

arxiv.org/abs/cond-mat/9803143v1

Physics

Condensed Matter

Statistical Mechanics

18 pages of text, RevTeX, additional 8 figures in 12 PS files

Scientific paper

10.1103/PhysRevE.58.303

Universality in isotropic, abelian and non-abelian, sandpile models is examined using extensive numerical simulations. To characterize the critical behavior we employ an extended set of critical exponents, geometric features of the avalanches, as well as scaling functions describing the time evolution of average quantities such as the area and size during the avalanche. Comparing between the abelian Bak-Tang-Wiesenfeld model [P. Bak, C. Tang and K. Wiensenfeld, Phys. Rev. Lett. 59, 381 (1987)], and the non-abelian models introduced by Manna [S. S. Manna, J. Phys. A. 24, L363 (1991)] and Zhang [Y. C. Zhang, Phys. Rev. Lett. 63, 470 (1989)] we find strong indications that each one of these models belongs to a distinct universality class.

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