Ising spins and disorder at the critical temperature $T_c$ (which increases with increasing value of $D$, yielding in the limit $D \longrightarrow + \infty$ the critical temperature of the 3d Ising model), whereas the xy–components form a classical three-dimensional plane-rotator disordering at the temperature[@Fer73] $T_{xy} = 2.2 J'$ (setting the Boltzmann constant equal to one).

Note that the specific heat does not vanish when $T$ approaches 0. This is an artefact of the classical nature of the planar spin components yielding $\lim_{T \to 0} C = \frac{1}{2}$.

In presence of the nondiagonal two–spin exchange with coupling constant $J^1_{xz}$ (Equation (5)), the ordering temperature $T_c$ of the axial spin components is decreased, see Figure 2. This results from the coupling, at temperatures above $T_{xy}$, of the ordered $z$–components to the disordered planar components, yielding additional fluctuations which lead to a decrease of the ordering temperature of the axial spin components. The value of $T_{xy}$ is not affected by this nondiagonal spin–exchange, as long as $\left| J^1_{xz} \right|$ is not too large, see below. The spin exchange involving products of squares of spins (Equation (6)) also leads to a decrease of $T_c$ for negative values of $J^2_{xz}$. This second coupling is not 