Figure 1 shows the temperature dependent specific heat and the magnetization obtained for vanishing nondiagonal spin exchange for the ferromagnetic model, with $J = J'$, $D = 3 J'$, and $H_x = 0$. The specific heat has a two peak structure, see Figure 1a: the peak at $T_c$ is the critical peak resulting from the disordering of the $z$–components of the spins, whereas the low–temperature peak at $T_{xy}$ follows from the disordering of the planar spin components. The magnetization data, see Figure 1b, show that the $z$–components, in absence of a coupling between planar and axial spin components, are not affected by this disordering.

This two peak structure of the specific heat should be compared to the specific heat of the classical anisotropic Heisenberg model showing only one maximum. For vanishing single–ion anisotropy the two peaks of the specific heat of the semi–classical model merge to a single peak located at the critical temperature of the corresponding classical isotropic Heisenberg model.

It is clear from Figure 1 that, due to the discretization of $S^z$ and the presence of the single–ion anisotropy, the disorderings of the axial and planar spin components are largely decoupled. The $z$–components behave like S = 1 