Scaling theory of self-organized criticality.

We study the phenomena of self-organized criticality originally proposed by Bak, Tang, and Wiesenfeld. A continuous-energy model is introduced. Using numerical simulations, we find that energy is homogeneously and isotropically distributed in space, and that it is concentrated around discrete values. We propose a scaling theory to estimate the various exponents. The activation cluster size distribution is found to be D(s)\ensuremath{\sim}1/${s}^{\ensuremath{\tau}}$, \ensuremath{\tau}=2-2/d; and the dispersion relation t\ensuremath{\sim}${r}^{z}$, z=(d+2)/3.