Dynamic scaling: Distinguishing self-organized from generically critical systems

The dynamic scaling approach separates nonequilibrium critical phenomena into two distinct categories: (a) those that are ‘‘generically’’ critical due to symmetry and (b) those that are self-organized critical. This phenomenological approach is demonstrated in the context of interface growth and depinning, where the surface width obeys the scaling form W(L,s₀,s₀+s) =(s/L^d)^βF(s₀/L^D,s/L^D). The quantity L is the linear system size, s₀ is the total motion of the interface, and s is the amount of growth separating two configurations. In case (b) the function F has a nontrivial dependence on s₀/L^D reflecting a diverging correlation length, while in case (a) it does not.