Magnetic and superconductive states in the repulsive Hubbard model

It is shown that antiferromagnetic, ferromagnetic, and superconductive states are possible in the repulsive Hubbard model. The role of small denominators of the Green functions and the Van Hove saddle points in the phase transitions is discussed. It is shown that superconductivity is possible if and only if one of the Van Hove saddle points is situated near the Fermi level. The Cooper pairing arises in channels with odd angular momenta. (It is the $p$-pairing in the first approximation.) The optimal mutual position of the Van Hove saddle point and the Fermi level corresponding to the maximal critical temperature is found. The problem of the coexistence of superconductivity and ferromagnetism is discussed. Bibliography: 25 titles.