Long-time tails in two-dimensional cellular automata fluids

Mode-coupling theory is used to calculate the Green-Kubo time correlation functions for the two-dimensional Frisch-Hasslacher-Pomeau lattice-gas cellular automaton. An intermediate algebraic decay ∼1/t and an asymptotic decay ∼1/[t √ln(t) ] are found. The amplitudes for these decays are calculated and it is found that the contribution from diffusive modes associated with spurious conservation laws is significant. For the computer simulations in cellular automata fluids only the algebraic tail is relevant; the asymptotic tail dominates only on time scales large compared to ${10}^{10}$ mean free times.