even layers, were computed. Here, the odd, respectively even layers have the magnetization $m_z^1 = +1$, respectively $m_z^1 = -1$ at $T=0$. The applied axial field points in the “+”–direction, i.e. it tends to destabilize the even layers.

The ground state was always used as starting configuration for the simulations. In absence of a planar field component, the state with $S^x = 0$ was chosen among the infinity of degenerate ground states. Note that in this case one encounters, after initial relaxation, a metastable state, in which the system remains, possibly, for a long time, the time depending on the size of the system and the temperature. The computed planar spin components are then supposed to be very close to their values in the thermodynamic limit.

Thermal properties of the tetragonal models
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In this section, the thermal properties of the tetragonal ferromagnetic and antiferromagnetic models (see Equation (4)) are discussed. For a vanishing external field, the Hamiltonian of the antiferromagnetic model can be mapped in the usual way onto that of the ferromagnetic model. Therefore, I will in the following present for $H_x = 0$ simulations of the ferromagnetic model, the antiferromagnetic model being analyzed for $H_x \neq 0$.

