\left( 1 -\sqrt{2} \right) H_x}{4}$ the ground state is given by a ferromagnetic phase where the spins have only a planar component. A positive coupling constant $J^2_{xz}$ does not yield a new stable phase. The ground state of the tetragonal antiferromagnetic model in presence of a nondiagonal spin exchange can be discussed in similar terms. In the following it is always supposed that the nondiagonal coupling constant does not exceed the threshold value which leads to a new ground state.

The thermal properties of the different models were investigated by simulating systems consisting of $L \times L \times L$ Heisenberg spins, with $L$ ranging from 10 to 30. As the equilibration proved to be rather slow, the first $3 \times 10^4$ Monte Carlo steps per site were usually discarded. Simulations for up to 20 different realizations with different random numbers were performed in order to improve the statistics. Besides the energy $E$ and the specific heat $C$, the different components of the magnetization per layer, $m_x(i)$, $m_y(i)$, and $m_z(i)$, and, for the antiferromagnetic models, related quantities such as the sublattice magnetizations, $\vec{M}_1 =
\left( m_x^1, m_y^1, m_z^1 \right)$ and $\vec{M}_2 =
\left( m_x^2, m_y^2, m_z^2 \right)$, referring to odd and 