Universal persistence exponents in an extremally driven system
arXiv:cond-mat/0111213 · doi:10.1103/PhysRevE.65.027104
Abstract
The local persistence R(t), defined as the proportion of the system still in its initial state at time t, is measured for the Bak--Sneppen model. For 1 and 2 dimensions, it is found that the decay of R(t) depends on one of two classes of initial configuration. For a subcritical initial state, R(t)\sim t^{-θ}, where the persistence exponent θcan be expressed in terms of a known universal exponent. Hence θis universal. Conversely, starting from a supercritical state, R(t) decays by the anomalous form 1-R(t)\sim t^{τ_{\rm ALL}} until a finite time t_{0}, where τ_{\rm ALL} is also a known exponent. Finally, for the high dimensional model R(t) decays exponentially with a non--universal decay constant.
4 pages, 6 figures. To appear in Phys. Rev. E