A study of the 2D Hubbard model in the antiferromagnetic phase by means of the COM is reported in Ref. . In particular the following properties have been computed:
The COM results have been analyzed in relation with the ones obtained by:
One of the main results we obtained by analyzing the antiferromagnetic phase of the 2D Hubbard model is a - phase diagram, at half-filling and in absence of frustration, with three kind of transitions. We have a Mott-Heisenberg transition (i.e., a transition between a paramagnetic metal and an antiferromagnetic insulator) at low values of the Coulomb repulsion mainly driven by the temperature, with a finite critical value of the interaction at zero temperature. This is a real achievement with respect to many other formulations in which any non-zero interaction drives a magnetic order at zero temperature [62,65]. Then, we obtained a Mott-Hubbard transition (i.e., a transition between a paramagnetic metal and an paramagnetic insulator), which is almost insensitive to temperature, for high values of the Coulomb interaction. Finally, we found a transition between an antiferromagnetic insulator and a paramagnetic insulator driven by the temperature at high values of the Coulomb interaction. In this latter case the antiferromagnetic component of the central gap vanishes (i.e., the magnetization disappears and the gaps appearing in the Hubbard subbands close up), but the paramagnetic component remains finite. We also obtained many other interesting results like the heat magnetization phenomena  and a metal insulator transition away from half-filling.