TIME-DEPENDENT ONE-DIMENSIONAL SPIN-1 ISING SYSTEM WITH WEAK-COUPLING

A modified version of Glauber's one-dimensional spin relaxation model is applied to a spin-1 Ising chain in order to study the time dependen ce of the system in the weak-coupling limit. The individual spin-1 Isi ng particles are assumed to interact with the heat bath, which causes them to change their states randomly in time. Coupling between the par ticles is introduced through the assumption that the transition probab ilities for any one spin-1 Ising particle depends on the state of the neighboring spin-1 Ising particles. A special assumption about the rat e constants is chosen such that the average values of the dipole momen t will return to the equilibrium value. We establish the system of rat e equations for average values of the dipole and quadruple moments, as well as their coupling. The Ising interaction between the spin-1 part icles is assumed to be weak compared to the coupling with the heat res ervoir. In this way we can terminate the hierarchy and solve the probl em of a linear chain with periodic boundary conditions, using the Four ier transformation. The resulting secular equation determines two sets of relaxation times and two sets of eigenvectors. From this equation both relaxation times are determined by a perturbation method.