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)∼1/$s^{\tau }$, τ=2-2/d; and the dispersion relation t∼$r^z$, z=(d+2)/3.