Spin- Ising model by the cluster variation method and the path probability method

The spin- Ising model Hamiltonian with arbitrary bilinear (J) and biquadratic (K) pair interactions is studied by using the lowest approximation of the cluster variation method (LACVM) and the path probability method (PPM) with the point distribution. First, equilibrium properties of the model are presented briefly by using the LACVM in order to understand dynamics of the model easily. Then, the PPM with the point distribution is applied to the model and the set of nonlinear differential equations, which is also called the dynamic or rate equations, is obtained. These equations are solved by two different methods: the first one is the Runge–Kutta method and the second one is to express the solution of the equations by means of the flow diagram. The results are also discussed.