that in this case both $T_c$ and $T_{xy}$ are shifted to lower temperatures, the shift being larger for larger values of $\left| J^1_{xz} \right|$.

Interestingly, no jump in $M_z$ occurs when the second spin exchange with coupling constant $J^2_{xz}$ is considered. For all values of $J^2_{xz}$ yielding the ferromagnetic ground state with both planar and axial spin components, see above, $M_z$ changes continuously at $T_{xy}$.

Figure 4 shows the specific heat of the antiferromagnetic tetragonal model obtained when planar fields with different strengths are applied and only diagonal couplings are considered. Increasing the value of $H_x$ moves $T_{xy}$ to lower temperatures, whereas $T_c$ is not changed. In presence of a planar field unusual strong finite–size effects are observed when the planar spin components disorder, making it necessary to simulate at least systems of length $L = 20$ in order to get a reliable estimate of $T_{xy}$. These strong finite–size effects are due to the presence of the $S^z = 0$ states and do not show up for the corresponding classical plane–rotator, as I checked. Finally, one should notice that, in presence of the nondiagonal coupling (5) with the strength $J^1_{xz}$, the total magnetization in $z$–direction again changes discontinuously for values 