Exact persistence exponent for one-dimensional Potts models with parallel dynamics

We obtain θ_p(q) = 2θ_s(q) for one-dimensional q-state ferromagnetic Potts models evolving under parallel fully synchronous dynamics at zero temperature from an initially disordered state, where θ_p(q) is the persistence exponent for parallel dynamics and θ_s(q) = -1/8 + (2/π²)[cos ^-1{(2-q)/q(2)^1/2}]² is the persistence exponent under serial (asynchronous) dynamics. This result is a consequence of an exact, albeit non-trivial, mapping of the evolution of configurations of Potts spins under parallel dynamics to the dynamics of two decoupled reaction-diffusion systems.