Aging Exponents in Self-Organized Criticality

TL;DR

This paper investigates aging behavior in self-organized critical models, revealing a new critical exponent related to temporal correlations and aging, through extensive numerical simulations in one and two dimensions.

Contribution

The study introduces and measures a new aging exponent in self-organized critical models, expanding understanding of their dynamical properties.

Findings

Aging exponent r ≈ 0.45 in 1D Bak-Sneppen model

Aging exponent r ≈ 0.23 in 2D Bak-Sneppen model

Estimated r = 1/4 for the multi-trade model in both dimensions

Abstract

In a recent Letter [Phys. Rev. Lett. 79, 889 (1997) and cond-mat/9702054] we have demonstrated that the avalanches in the Bak-Sneppen model display aging behavior similar to glassy systems. Numerical results for temporal correlations show a broad distribution with two distinct regimes separated by a time scale which is related to the age of the avalanche. This dynamical breaking of time-translational invariance results in a new critical exponent, $r$. Here we present results for $r$ from extensive numerical simulations of self-organized critical models in $d=1$ and 2. We find $r_{d=1}=0.45\pm 0.05$ and $r_{d=2}=0.23\pm 0.05$ for the Bak-Sneppen model, and our results suggest $r=1/4$ for the analytically tractable multi-trade model in both dimensions.