should bear in mind when applying the present results to FeBr$_2$ that the Hamiltonian (1) may not be complete. Indeed, the recent measurements in an nonaxial field[@pet98] suggest the presence of in–plane anisotropy in FeBr$_2$, resulting, for example, from magnetoelastic couplings. Thus an anisotropy is not contained in the present Hamiltonian. Furthermore, one should recall that the treatment of the Heisenberg Hamiltonian is only approximative, due to the semi–classical approach adopted in Section II, leading to a strong decoupling between planar and axial spin components.

Nevertheless, the present study clearly shows the importance of the nondiagonal spin exchange and of the quantum nature of the S = 1 spins in describing the low-temperature properties of FeBr$_2$. Especially, the peculiar shape of the specific heat in an axial field may be traced back to a phase transition of the planar spin components, taking place, rather by chance, close to the anomaly of the axial spin components in the antiferromagnetic phase of FeBr$_2$.

Summary
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Recent experimental investigations showed some intriguing transition–like phenomena in the magnetization and in the specific heat of the layered antiferromagnet FeBr$_2$. The observed transverse spin–ordering in a nonaxial field suggests the existence of a nondiagonal exchange between 