Dynamic critical approach to self-organized criticality

KARINA LANERI ; ALEJANDRO F. ROZENFELD ; EZEQUIEL V. ALBANO

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Año: 2005 vol. 72 p. 1 - 4

1539-3755

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 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 τALL=0.39(2), in excellent agreement with values already accepted and obtained within the SOC regime.