Symmetries and Universality Classes in Conservative Sandpile Models

Details Symmetries and Universality Classes in Conservative Sandpile Models Symmetries and Universality Classes in Conservative Sandpile Models

1998-05-18

arxiv.org/abs/cond-mat/9805206v1

Physics

Condensed Matter

10 pages of text, RevTeX, additional 3 figures in 4 PS files

Scientific paper

The symmetry properties which determine the critical exponents and universality classes in conservative sandpile models are identified. This is done by introducing a set of models, including all possible combinations of abelian vs. non-abelian, deterministic vs. stochastic and isotropic vs. anisotropic toppling rules. The universality classes are determined by an extended set of critical exponents, scaling functions and geometrical features. Two universality classes are clearly identified: (a) the universality class of abelian models and (b) the universality class of stochastic models. In addition, it is found that non-abelian models with deterministic toppling rules exhibit non-universal behavior.

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