Dynamic Critical approach to Self-Organized Criticality

Original · EN

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 (ρ(t)) below the critical value, it is shown that i) starting the dynamics with configurations such that ρ(t=0) → 0 one observes an initial increase of the density with exponent θ= 0.12(2); ii) using initial configurations with ρ(t=0) → 1, the density decays with exponent δ= 0.47(2). It is also shown that he 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 τALL = 0.39(2), in excellent agreement with values already accepted and obtained within the SOC regime.