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-12 Ising model, it gives the same result as that of the Bethe–Peierls approximation, such as for the transition temperature. The formulation is also...

A new type of cluster theory in Ising models with an arbitrary spin S(S12) is presented by the use of the differential operator technique and Ising spin identities. The formulations for evaluating the transition line are derived for the two Ising systems with S=1 and 32 as well as for the spin-S...