The quantum critical behavior of antiferromagnetic itinerant systems with van Hove singularities of electronic spectrum

The interplay of magnetic and superconducting fluctuations in two dimensional systems with van Hove singularities in the electronic spectrum is considered within the functional renormalization group (fRG) approach. While the fRG flow has to be stoped at a certain minimal temperature T_RG^min, we study temperature dependence of magnetic and superconducting susceptibilities both, above and below T_RG^min, which allows to obtain the resulting ground state phase diagram. Close to half filling the fRG approach yields two quantum phase transitions: from commensurate antiferromagnetic to incommensurate phase and from the incommensurate to paramagnetic phase, the region of the commensurate magnetic phase is possibly phase separated away from half filling. Similarly to results of Hertz-Moriya-Millis approach, the temperature dependence of the inverse (incommensurate) magnetic susceptibility at the quantum phase transition from incommensurate to paramagnetic phase is found almost linear in temperature.