The spin-1/2 anisotropic Heisenberg model with antiferromagnetic exchange interactions in the presence of a external magnetic field and a Dzyaloshinskii-Moriya interaction is studied by employing the usual mean-field approximation. The magnetic properties are obtained and it is shown that only second-order phase transitions take place for any values of the theoretical Hamiltonian parameters. Contrary to previous results from effective field theory, no anomalies have been observed at low temperatures. However, some re-entrancies still persist in some region of the phase diagram.

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Magnetic phenomena of the superantiferromagnetic Ising model in both uniform longitudinal (H) and transverse (Ω) magnetic fields are studied by employing a mean-field variational approach based on Peierls-Bogoliubov inequality for the free energy. A single-spin cluster is used to get the approximate thermodynamic properties of the model. The phase diagrams in the magnetic fields and temperature (T ) planes, namely, H − T and Ω − T , are analyzed on an anisotropic square lattice for some values of the ratio α = J y /J x , where J x and J y are the exchange interactions along the x and y directions, respectively. Depending on the range of the Hamiltonian parameters, one has only second-order transition lines, only first-order transition lines, or first-and second-order transition lines with the presence of tricritical points. The corresponding phase diagrams show no reentrant behavior along the first-order transition lines at low temperatures. These results are different from those obtained by using Effective Field Theory with the same cluster size.