Superconductivity and antiferromagnetism in cuprates and pnictides: Evidence of the role of Coulomb correlation

•In a layered 2D cuprates the long-range order antiferromagnetism is driven mainly by the Van Hove singularity.•The long-range antiferromagnetism quickly disappear with doping away from the Van Hove singularity.•For pnictides the antiferromagnetism exists as a result of the nesting condition.•Since the doping steadily changes the nesting conditions, the antiferromagnetism and superconductivity may coexist. We consider the Hubbard model in terms of the perturbative diagrammatic approach (UNF⩽1) where the interaction between two electrons with antiparallel spins in the lowest order of perturbation is described by the short-range repulsive contact (on-site) interaction (U>0). We argue that in layered 2D cuprates the long-range order antiferromagnetism is driven mainly by the Van Hove singularity, whereas in the case of pnictides the antiferromagnetism exists as a result of the nesting condition. We show that when the interaction is quite strong (UNF≈1) in the case of the Van Hove singularity the electron system undergoes the antiferromagnetic phase transition with the log-range order parameter and large insulating gap. The long-range antiferromagnetism quickly disappear, as shown, with the doping away from the Van Hove singularity, but the antiferromagnetic short-range correlation persists (UNF