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

A new type of cluster theory in Ising models with an arbitrary spin S(S>12) 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 transverse Ising systems. The statistical accuracy of the result is the so-called extension of the spin-12 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).