Non-Markovian persistence and nonequilibrium critical dynamics

The persistence exponent θ for the global order parameter $M(t)$ of a system quenched from the disordered phase to its critical point describes the probability, p(t)~t^-θ, that $M(t)$ does not change sign in the time interval t following the quench. We calculate θ to O(ε²) for model A of Hohenberg and Halperin [Rev. Mod. Phys. 49, 435 (1977)] (and to order ε for model C) and show that at this order $M(t)$ is a non-Markov process. Consequently, to our knowledge, θ 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)].