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)similar to wt(-theta), that M(t) does not change sign in the time interval t following the quench. We calculate theta to 0 (epsilon(2)) for model A of Hohenberg and Halperin [Rev. Mod. Phys. 49, 435 (1977)] (and to order epsilon for model C) and show that at this order M(t) is a non-Markov process. Consequently, to our knowledge, 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 (1995)].