MAPPING SELF-ORGANIZED CRITICALITY ONTO CRITICALITY

We present a general conceptual framework for self-organized criticality (SOC), based on the recognition that it is nothing but the expression, ''unfolded'' in a suitable parameter space, of an underlying unstable dynamical critical point. More precisely, SOC is shown to result from the tuning of the order parameter to a vanishingly small, but positive value, thus ensuring that the corresponding control parameter Lies exactly at its critical value for the underlying transition. This clarifies the role and nature of the very slow driving rate common to all systems exhibiting SOC. This mechanism is shown to apply to models of sandpiles, earthquakes, depinning, fractal growth and forest fires, which have been proposed as examples of SOC.