Laws for Stationary States in Systems with Extremal Dynamics

Abstract

Laws are derived for stationary states in self-organized critical systems with extremal dynamics. In a class of models, the exponent $\eta$ for the survival of activity is zero in all dimensions. Scaling relations for other critical exponents are found. Numerical simulations of Sneppen's interface depinning model, Zaitsev's low temperature creep model, and the Bak-Sneppen evolution model agree with these predictions.