Non-Markovian persistence at the parity conserving point of a one-dimensional nonequilibrium kinetic Ising model

One-dimensional nonequilibrium kinetic Ising models evolving under the competing effect of spin-hips at zero temperature and nearest-neighbour spin exchanges exhibiting a parity-conserving (PC) phase transition on the level of kinks are investigated here numerically from the point of view of the underlying spin system. The dynamical persistency exponent Theta and the exponent lambda characterizing the two-time autocorrelation function of the total magnetization under nonequilibrium conditions are reported. It is found that the critical fluctuations at the PC transition have a strong effect on the spins: the behaviour becomes non-Markovian and the above exponents exhibit drastic changes as compared with the Markovian Glauber-Ising case. In this context the crucial importance of considering the global order parameter (instead of the local one) is emphasized.