Differential operator technique for higher spin problems

Differential Operator Technique in the Ising Spin Systems

“…Substituting Szi = -S,...,+S into (129), one can get a set of (2S+ 1) parameters for the spin variables as well as the coefficients An(a), like (128) [30].…”

“…In order to take account of the lattice dimensionality as well as the coordination number, one has to treat the multispin correlation functions in forms depending on these qualities. Such a formulation can be made by going to Matsudaira,s higher order decoupling approximation [3] better than the simple decoupling approximation (30). Then, the formulation cannot be described in a general form but it must be made separately in a way of depending on the lattice structure.…”

“…We are now in a position to clarify the background why the simple decoupling approximation (30) improves the standard MFA (14). For H = 0.0, Eq.…”

“…To proceed further, one has to make some approximations, in order to treat the identities approximately. The simplest approximation, and the one most frequently adopted, is to decouple these according to Introducing the approximation (30), the averaged value of μi ((23) with 1.0) can be written in a compact form [6]:…”

“…4.1 we have introduced a simple decoupling method (30) for treating the multispin correlation functions. In this part, we shall discuss how the formulation of Sec.…”