Magnetic fluctuations and itinerant ferromagnetism in two-dimentional systems with van Hove singularities

We use the quasistatic approach to analyze the criterion of ferromagnetism for two-dimentional (2D) systems with the Fermi level near Van Hove singularities (VHS) of the electronic spectrum. It is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction I between electrons and paramagnons, which corresponds to the Hubbard on-site repulsion U , is sufficiently large. The critical interactions Ic and Uc remain finite at Van Hove filling and exceed considerably their values obtained from the Stoner criterion due to incommensurate spin fluctuations, which are important near the ferromagnetic quantum phase transition. Combining the quasistatic approximation and the equation of motion method for the Green function we obtain the results for the electronic self-energy to first order in the inverse number of spin components.