0$, yielding thermal properties similar to the S = 1 Ising model.

The ground states of the semi–classical antiferromagnetic hexagonal and tetragonal models are readily obtained provided the nondiagonal exchange constant is not too large. In small axial fields ($H_x = 0$ and $H_z < H_z^c = -2 N J'$, $N = 10$ for the hexagonal model and $N = 2$ for the tetragonal model), the antiferromagnetic phase, where the spins are aligned ferromagnetically in the layers, with an antiferromagnetic arrangement between subsequent layers, is stable. For larger fields ($H_z > H_z^c$ and $H_x=0$) the axial spin components $S^z$ order ferromagnetically, whereas the signs of the planar components ($S^x$ and $S^y$) still change from layer to layer. Note that in absence of an ordering planar field the ground state is infinitely degenerate, as the angle between the planar spin components and, say, the $x$–axis is not fixed. Keeping $H_z$ constant and applying a planar field, $H_x$, yields a stable phase where the $xy$–components of the spins are ordered in a spin–flop phase, in which the magnetization per layer in $x$–direction has the same value in each layer, whereas the $y$–components have different signs in adjacent layers but the same absolute 