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

Abstract. One-dimensional nonequilibrium kinetic Ising models evolving under the competing effect of spin–flips 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 2 and the exponent 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. In recent years, two nonequilibrium dynamical critical exponents have been discovered, which arise under nonequilibrium conditions. The nonequilibrium (short-time) exponent characterizes two-time correlations in systems relaxing to their critical state in the process of quenching from infinitely high temperatures to Tc [1, 2]. Recently, one more critical exponent was proposed [3], the persistence exponent 2, associated with the probability p.t / / t−2, that the global order parameter has not changed sign up to time t after a quench to the critical point [4]. For some known examples, cited in [4], the scaling law 2Z D − d C 1 −