A new type of cluster theory in Ising models (I)

A new type of cluster theory in Ising models is presented by the use of differential operator technique and Ising spin identity. In the spin- Ising model, it gives the same result as that of the Bethe–Peierls approximation, such as for the transition temperature. The formulation is also applied to the investigation of phase diagrams in both the spin- transverse Ising model and the spin-1 Ising system with a single-ion anisotropy.