Landau-Ginzburg Theory of Self-Organized Criticality

Abstract

Self-organized criticality occurs through a nonlinear feedback mechanism triggering transitions between different metastable states. These transitions take the form of intermittent avalanchelike events distributed according to a power law. We present the first and simplest fully continuous partial differential formalism of this phenomenon, based on the introduction of a subcritical dynamics. SOC is identified as the regime where diffusive relaxation is faster than the instability growth rate. In the other limit of slow diffusion, avalanches comparable to the system size become dominant. This provides a general correspondence between SOC and synchronization of threshold oscillators.