Exact solution for the higher correlation functions of the linear spin-1 Ising model

The one-dimensional Ising problem for spin $S=1$ is solved by the method of two-time Green's functions. The chain of equations of motion admit exact decoupling and they lead to a set of exact relationships for the correlation functions, which are investigated by the “method of difference equations”. The general form of the spatial structure of the correlation functions is determined in the absence of an external magnetic field, and the main physical characteristics are obtained for an infinite chain of spins.