Critical Behavior of the Spin System with Anisotropic Exchange Interactions. I.

Abstract

The spin system described by the Hamiltonian
(Remark: Graphics omitted.),
is investigated by the three different methods: the effective Hamiltonian method, the spin wave theory, and the Green function method. The system is reduced to the Ising model when ξ=η=0, the Heisenberg model when ξ=η=1, and XY model when ξ=1, η=0, respectively. The variation of the Curie point T_c with ξ and η is determined for the two- and three-dimensional lattices. In the three-dimensional lattice, T_c of the XY model lies between those of the Ising and Heisenberg model. On the other hand, in the two-dimensional lattice, the spontaneous magnetization is absent in the XY model and Heisenberg model and further the model intermediate between them.