Fixed scale transformation approach to the nature of relaxation clusters in self-organized criticality

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Abstract
We use the fixed scale transformation method, developed for fractal growth, to investigate analytically the nature of clusters in self-organized criticality (SOC). In two dimensions the clusters of sites involved in a relaxation process turn out to be compact (D=2) because of the absence of effective screening. Therefore they are more similar to Eden-type clusters (possibly with a rough surface) than to those of the usual fractal growth models. This result is in good agreement with the computer simulations and one can conjecture that it should hold for any dimensions. The critical state corresponding to SOC dynamics is therefore of much simpler nature with respect to those of the usual fractal growth models.

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