Non-Markovian Persistence and Nonequilibrium Critical Dynamics

The persistence exponent \theta for the global order parameter, M(t), of a system quenched from the disordered phase to its critical point describes the probability, p(t) \sim t^{-\theta}, that M(t) does not change sign in the time interval t following the quench. We calculate \theta to O(\epsilon^2) for model A of critical dynamics (and to order \epsilon for model C) and show that at this order M(t) is a non-Markov process. Consequently, \theta is a new exponent. The calculation is performed by expanding around a Markov process, using a simplified version of the perturbation theory recently introduced by Majumdar and Sire [Phys. Rev. Lett. _77_, 1420 (1996); cond-mat/9604151].