Global Persistence Exponent for Nonequilibrium Critical Dynamics

A “persistence exponent” $\theta$ is defined for nonequilibrium critical phenomena. It describes the probability, $p\left(t\right)\sim t^{-\theta }$, 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 $O\left(n\right)$ model, to first order in $\epsilon =4-d$, and for the 1D Ising model. Numerical results are obtained for the 2D Ising model. We argue that $\theta$ is a new independent exponent.