M. Keskin et Phe. Meijer, TIME-DEPENDENT ONE-DIMENSIONAL SPIN-1 ISING SYSTEM WITH WEAK-COUPLING, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 55(5), 1997, pp. 5343-5349
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.