Global Persistence Exponent for Critical Dynamics

Abstract

A `persistence exponent' $θ$ is defined for nonequilibrium critical phenomena. It describes the probability, $p(t) \sim t^{-θ}$, that the global order parameter has not changed sign in the time interval $t$ following a quench to the critical point from a disordered state. This exponent is calculated in mean-field theory, in the $n=\infty$ limit of the $O(n)$ model, to first order in $ε= 4-d$, and for the 1-d Ising model. Numerical results are obtained for the 2-d Ising model. We argue that $θ$ is a new independent exponent.