Driving, conservation and absorbing states in sandpiles

Alessandro Vespignani, Ronald Dickman, Miguel A. Munoz, Stefano Zapperi

Published 1998-06-21, updated 1998-11-11Version 2

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.