MULTIFRACTAL GENERATION OF SELF-ORGANIZED CRITICALITY

We clarify the links between scaling and self-organized criticality in demonstrating that multifractal processes -with nonvanishing input reach self-organized criticality via the analog of a first order phase transition. We emphasize that the first order transitions are intrinsic consequences of the scale and dimension of the observations, whereas second order transitions arise from finite sample sizes. We point out implications and applications for nonlinear physical systems.