Persistence in One-dimensional Ising Models with Parallel Dynamics

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We study persistence in one-dimensional ferromagnetic and anti-ferromagnetic 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) 1/tᵗhetaₚ with thetaₚ ≃ 0.75 numerically. A mapping to the dynamics of two decoupled A+A → 0 models yields thetaₚ = 3/4 exactly. A finite size scaling analysis clarifies the nature of dynamical scaling in the distribution of persistent sites obtained under this dynamics.