Persistence in one-dimensional Ising models with parallel dynamics

We study persistence in one-dimensional ferromagnetic and antiferromagnetic nearest-neighbor Ising models with parallel dynamics. The probability P(t) that a given spin has not flipped up to time t, when the system evolves from an initial random configuration, decays as P(t)similar to1/t(theta p) with theta (p) similar or equal to 0.75 numerically. A mapping to the dynamics of two decoupled A + A --> 0 models yields theta (p) = 3/4 exactly. A finite size scaling analysis clarifies the nature of dynamical scaling in the distribution of persistent sites obtained under this dynamics.