CRITICAL PHASE-TRANSITIONS MADE SELF-ORGANIZED - A DYNAMIC SYSTEM FEEDBACK MECHANISM FOR SELF-ORGANIZED CRITICALITY

According to Kadanoff, self-organized criticality (SOC) implies the operation of a feedback mechanism that ensures a steady state in which the system is marginally stable against a disturbance. Here, we extend this idea and propose a picture according to which SOC relies on a non-linear feedback of the order parameter on the control parameter(s), the amplitude of this feedback being tuned by the spatial correlation length xi. The self-organized nature of the criticality stems from the fact that the limit xi --> + infinity is attracting the non-linear feedback dynamics. It is applied to known self-organized critical systems such as << sandpile >> models as well as to a simple dynamical generalization of the percolation model. Using this feedback mechanism, it is possible in principle to convert standard << unstable >> critical phase transitions into self-organized critical dynamics, thereby enlarging considerably the number of models presenting SOC. These ideas are illustrated on the 2D Ising model and the values of the various << avalanche >> exponents are expressed in terms of the static and dynamic Ising critical exponents.