order, at larger couplings this model converges to the same ${\bf Q}_{AF}=(1,0)$ order [@nicholson]. ](Fig3R2)

Hubbard model investigations provide additional insight on this subject. When compared with similar efforts for the cuprates, the study of Hubbard models for the pnictides is far more challenging because several Fe orbitals are needed. For this reason, many efforts are restricted to mean-field Hartree-Fock approximations. For the undoped three-orbital Hubbard model, employing the $d_{xz}$, $d_{yz}$, and $d_{xy}$ orbitals of relevance at the FS, a sketch of a typical mean-field phase diagram varying $U$ and the Hund coupling $J_H$ [@qluo10] is in Fig. 3a. Three regimes are identified: a small $U$ phase where the state is paramagnetic, followed with increasing $U$ by an intermediate regime simultaneously metallic and magnetic [@qluo10], and finally a large-$U$ phase where a gap in the density-of-states (DOS) is induced leading to an insulator (with concomitant orbital order). Comparing the theoretical predictions for the magnetic moment in the ${\bf Q}_{AF}=(1,0)$ wave-vector channel against neutrons, and the one-particle spectral function $A({\bf k},\omega)$ against ARPES, the intermediate-coupling region dubbed “physical region” in yellow in Fig. 3a represents qualitatively the undoped BaFe$_{2-x}T_x$As$_2$ compounds [@qluo10]. In this regime, $U/W\sim$0.3-0.4, and similar results were reported for 