Dynamic Behavior of a Spin-1 Ising Model. Relaxation of Order Parameters and the `Flatness' Property of Metastable States
Dynamic behavior of a spin-1 Ising model  with arbitrary bilinear (J) and biquadratic (K) pair interactions is studied by using the path probability method . First the equilibrium behavior of the model is given briefly in order to understand the nonequilibrium behavior. Then the path probability method is applied to the spin-1 Ising model with J and K Hamiltonian and the system of nonlinear differential equations, which are also called the dynamic equations or rate equations, is found. The dynamic equations are solved using the Runga-Kutta method and the solutions, namely relaxation of order parameters are examined to see the "flatness" property of metastable states. It is found that the system relaxes to either stable or metastable states depending upon the initial values of the order parameters. Moreover, if there are more than one metastable states, the relaxation occurs according to the initial values of the order parameters or free energy values. Finally, the results are compared with the flow diagrams which are the solutions of the dynamic equations in two-dimensional phase space  and it is seen that the same results are found except for the "flatness" property of metastable states.
KESKİN, Mustafa and ERDEM, Rıza (1997) "Dynamic Behavior of a Spin-1 Ising Model. Relaxation of Order Parameters and the `Flatness' Property of Metastable States," Turkish Journal of Physics: Vol. 21: No. 1, Article 25. Available at: https://journals.tubitak.gov.tr/physics/vol21/iss1/25