Driving, conservation and absorbing states in sandpiles

Abstract

We use a phenomenological field theory, reflecting the symmetries and conservation laws of sandpiles, to compare the driven dissipative sandpile, widely studied in the context of self-organized criticality, with the corresponding fixed-energy model. The latter displays an absorbing-state phase transition with upper critical dimension $d_c=4$. We show that the driven model exhibits a fundamentally different approach to the critical point, and compute a subset of critical exponents. We present numerical simulations in support of our theoretical predictions.

12 pages, 2 figures; revised version with substantial changes and improvements

References in corpus (5)

• How self-organized criticality works: A unified mean-field picture
• Self-organized criticality as an absorbing-state phase transition
• Universality Classes in Isotropic, Abelian and non-Abelian, Sandpile Models
• Mean-field behavior of the sandpile model below the upper critical dimension
• Logarithmic corrections of the avalanche distributions of sandpile models at the upper critical dimension

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