Spin fluctuations and ferromagnetic order in two-dimensional itinerant systems with Van Hove singularities

The quasistatic approach is used to analyze the criterion of ferromagnetism for two-dimensional (2D) systems with the Fermi level near Van Hove (VH) singularities of the electron spectrum. It is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction between electrons and paramagnons, determined by the Hubbard on-site repulsion U, is sufficiently large. Due to incommensurate spin fluctuations near the ferromagnetic quantum phase transition, the critical interaction Uc remains finite at VH filling and exceeds considerably its value obtained from the Stoner criterion. A comparison with the functional renormalization group results and mean-field approximation which yields a phase separation is also performed.