Nonequilibrium Phase Transitions in a Driven Sandpile Model

Abstract

We construct a driven sandpile slope model and study it by numerical simulations in one dimension. The model is specified by a threshold slope $σ_c\/$, a parameter $α\/$, governing the local current-slope relation (beyond threshold), and $j_{\rm in}$, the mean input current of sand. A nonequilibrium phase diagram is obtained in the $α\, -\, j_{\rm in}\/$ plane. We find an infinity of phases, characterized by different mean slopes and separated by continuous or first-order boundaries, some of which we obtain analytically. Extensions to two dimensions are discussed.