Universal persistence exponents in an extremally driven system.

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 one and two 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) equivalent to t(-theta), where the persistence exponent theta can be expressed in terms of a known universal exponent. Hence theta is universal. Conversely, starting from a supercritical state, R(t) decays by the anomalous form 1-R(t) equivalent to t(tau(all)) until a finite time t(0), where tau(all) is also a known exponent. Finally, for the high dimensional model R(t) decays exponentially with a nonuniversal decay constant.