SELF-ORGANIZED CRITICALITY IN SANDPILES - NATURE OF THE CRITICAL PHENOMENON

We identify the avalanche boundaries in a class of sandpile models, and derive their dynamics, which consist of birth, death, and coalescence events. We then introduce and study a simple trough model based on these boundary dynamics. We prove that the trough model has a phase transition, and that at and below the critical point, troughs become extinct in the thermodynamic limit. Numerical results suggest that sandpile models are associated with such a critical point, and that the observed scaling behavior results from finite-size effects. © 1990 The American Physical Society.