Dynamic critical approach to self-organized criticality

A dynamic scaling ansatz for the approach to the self-organized critical (SOC) regime is proposed and tested by means of extensive simulations applied to the Bak-Sneppen model (BS), which exhibits robust SOC behavior. Considering the short-time scaling behavior of the density of sites [rho(t)] below the critical value, it is shown that (i) starting the dynamics with configurations such that rho(t=0)-->0 one observes an initial increase of the density with exponent theta=0.12(2); (ii) using initial configurations with rho(t=0)-->1, the density decays with exponent delta=0.47(2). It is also shown that the temporal autocorrelation decays with exponent Ca=0.35(2). Using these dynamically determined critical exponents and suitable scaling relationships, all known exponents of the BS model can be obtained, e.g., the dynamical exponent z=2.10(5), the mass dimension exponent D=2.42(5), and the exponent of all returns of the activity tauALL=0.39(2), in excellent agreement with values already accepted and obtained within the SOC regime.