Dynamics of the spin-1 Ising mean field model

A spin-1 Ising system with dipolar and quadrupolar interactions is placed in contact with a phonon heat bath. Using the projection operator formalism of Zwanzig and Nakajima, a master equation on the time scale of one microscopic event is derived from the Liouville equation. The transition rates thus obtained depend upon the detailed dynamics of the system, bath, and interactions between the two. Coarse-graining removes these details and yields a phenomenological transition rate similar to the form proposed by Langer. The kinetic equations which describe the most and least likely temporal evolution of the system are then derived. Finally, the time dependence of the two order parameters which characterize the system is examined numerically.