Critical Exponents and Scaling Relations for Self-Organized Critical Phenomena

Abstract

Critical indices $\beta$, $\gamma$ $\delta$, $\nu$, etc. are defined and calculated for self-organized critical phenomena. Scaling relations are derived and checked numerically. The order-parameter exponent $\beta$ describes the spontaneous current and the relaxation to the critical point. The power spectrum has "$\frac{1}{f}$" behavior with exponent $\phi =\frac{\gamma }{\nu z}$, where $z$ is the dynamical critical exponent.