in S = 1 models.

In the present work, I shall present a Monte Carlo study of S = 1 anisotropic Heisenberg models which include a nondiagonal exchange term between axial and planar spin components. The quantum nature of the S = 1 spins will be taken into account in a semi–classical approximation. Especially, I shall give a possible explanation of the peculiar shape of the specific heat of FeBr$_2$ and discuss the spin–ordering in an axial and in a nonaxial field.

The paper is organized in the following way: In Section II the anisotropic S = 1 Heisenberg models are introduced and the semi–classical approximation used in the simulations is discussed. Section III deals with the properties of ferromagnetic and antiferromagnetic models on a tetragonal lattice. These simplified models are studied in order to investigate the effects of (1) the semi–classical approximation, (2) different couplings between planar and axial spin components, and (3) an external planar field component. In Section IV a realistic model for FeBr$_2$, both in an axial and in a tilted field, is discussed and the findings are compared to the experiments. Some of the results of this Section have already been published in a brief 