of $\left| J^1_{xz} \right|$ larger than the threshold value, which seems not to depend on the value of $H_x$.

Thermal properties of the hexagonal model
=========================================

Most of the features discussed in the previous Section for the tetragonal models are also encountered if the realistic hexagonal model (1) for FeBr$_2$ is considered.[@ple98] In the following I will not reiterate the discussion on the values of the diagonal couplings of the spins (the interested reader is referred to Ref. 9) and choose a set of parameters, based on inelastic neutron scattering experiments[@yel75; @pou93], for which pronounced anomalies in the magnetization data and in the specific heat data are observed[@ple97]: $J_1 = -16.75 J'$, $J_2 = 0$, $J_3 = -0.29 J_1$, and $\eta = 0.78$.

Figure 5 shows the specific heat and the sublattice magnetizations obtained for strong single–ion anisotropy $D$ and vanishing nondiagonal interactions, with $H_z = -18 J'$ and $H_x = 0$. The temperature dependent specific heat $C(T)$ has a three peak structure: the peak at $T_c$ is the critical peak resulting from the disordering of the $z$–components of the spins. Going to lower temperatures, one encounters first the anomaly due to the noncritical spin fluctuations. This peak does not 