Time dependence of the weakly coupled spin-1 Ising system using the Glauber model

We study the time dependence of the one-dimensional weakly coupled spin-1 Ising system by means of the modified version of Glauber's one-dimensional spin relaxation model and the system of dynamic equations for the one- and two-points functions is derived. We solve the dynamic equations analytically and find the exact solutions for the relaxation times in the weak coupling limit. We also make a comparison with the relaxation times which were found by a first-order perturbation method.