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The interplay of magnetic and superconducting fluctuations in two dimensionalsystems with van Hove singularities in the electronic spectrum is consideredwithin the functional renormalization group (fRG) approach. While the fRG flowhas to be stoped at a certain minimal temperature T_RG^min, we studytemperature dependence of magnetic and superconducting susceptibilities both,above and below T_RG^min, which allows to obtain the resulting ground statephase diagram. Close to half filling the fRG approach yields two quantum phasetransitions: from commensurate antiferromagnetic to incommensurate phase andfrom the incommensurate to paramagnetic phase, the region of the commensuratemagnetic phase is possibly phase separated away from half filling. Similarly toresults of Hertz-Moriya-Millis approach, the temperature dependence of theinverse (incommensurate) magnetic susceptibility at the quantum phasetransition from incommensurate to paramagnetic phase is found almost linear intemperature.

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