A new type of cluster theory in Ising systems (II)

A new type of cluster theory in Ising models with an arbitrary spin 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 as well as for the spin-S transverse Ising systems. The statistical accuracy of the result is the so-called extension of the spin- Bethe–Peierls approximation to the spin-S system. Numerical results are performed and analyzed for the systems with three coordination numbers z (z=3,4 and 6).