so effective in destabilizing the ferromagnetically ordered $z$–components, yielding a smaller decrease of $T_c$.

If the strength of $\left| J^1_{xz} \right|$ is increased beyond a threshold value (being around 0.65 $J'$ for $J = J'$ and $D= 3 J'$), a jump in the axial component of the magnetization, $M_z$, is observed, see Figure 3a. This discontinuous change, which is induced by the disordering of the planar components, shows up as a sharp peak in the specific heat (Figure 3b). At temperatures slightly above $T_{xy}$ some orderness of the $z$–components still persists, i.e. $M_z \neq 0$. Increasing further the temperature, $M_z$ increases until, at $T_c$ (= 3.1 $J'$ for the parameters of Figure 3), the disordering of the $z$–components finally takes place, yielding a second peak in the specific heat. This behaviour of $M_z$ may be better understood when the temperature, starting from the disordered high temperature phase, is decreased. At $T_c$, the $z$–components order at the usual second order phase transition. The increase of the ordering of the $S^z$ spins at temperatures below $T_c$ increases the effect of the nondiagonal exchange, yielding, after an initial slow rising, effectively a decrease of $M_z$, until, at $T_{xy}$, the planar components order. Note 