  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.
