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 ${d}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4$. 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.