Equilibrium and nonequilibrium behavior of the spin-1 Ising model in the quadrupolar phase

Equilibrium properties of the spin-1 Ising model with the arbitrary bilinear (J) and biquadratic (K) pair interactions are studied on a body centered cubic lattice by using the pair approximation of the cluster variation method, which is identical to the Bethe approximation, in the quadrupolar phase. First, the thermal variation of the metastable and unstable dipole and quadrupolar moment order parameters is investigated and the metastable and unstable branches of them are found besides the stable branch of the quadrupolar moment order. In addition, it is found that when the values of α=J/K decreases, transition temperatures also decrease and some of metastable and unstable branches of order parameters disappear. On the other hand, nonequilibrium behavior of the model in the quadrupolar phase is studied by using the path probability method and the set of nonlinear differential equations, which is also called the dynamic or rate equations, is obtained. The solutions of the dynamic equations are expressed by means of flow diagrams near the transition temperatures. The stable, metastable and unstable solutions are shown and the “overshooting” phenomenon is seen in the flow diagrams, explicitly. The role of the unstable points, as separators between the stable and the metastable points, is described and how a system freezes in a metastable state is also investigated, extensively.