Sandpiles, avalanches, and the statistical mechanics of nonequilibrium stationary states

Abstract

The scaling properties of three nontrivial one-dimensional avalanche models are analyzed. The first two of them are the local limited model with one open, one closed, and with periodic boundary conditions, respectively. A theory for the scaling properties of these models based on the existence of two fundamental length scales, which diverge in the thermodynamic limit, is developed. The third model studied is a trapless version of the nonperiodic local limited model. We find that it is scale invariant. Our theoretical predictions are compared with extensive computer simulations in all three cases.