Fractal properties of relaxation clusters and phase transition in a stochastic sandpile automaton

S. Luebeck; K. D. Usadel; B. Tadic

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Fractal properties of relaxation clusters and phase transition in a stochastic sandpile automaton

S. Luebeck·K. D. Usadel·B. Tadic

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Abstract

We study numerically the spatial properties of relaxation clusters in a two dimensional sandpile automaton with dynamic rules depending stochastically on a parameter p, which models the effects of static friction. In the limiting cases p=1 and p=0 the model reduces to the critical height model and critical slope model, respectively. At p=p_c, a continuous phase transition occurs to the state characterized by a nonzero average slope. Our analysis reveals that the loss of finite average slope at the transition is accompanied by the loss of fractal properties of the relaxation clusters.

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S. Luebeck, K. D. Usadel, B. Tadic. 1995-02-24. Fractal properties of relaxation clusters and phase transition in a stochastic sandpile automaton. https://arxiv.org/abs/cond-mat/9502107

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