Antiferromagnetism, ferromagnetism and superconductivity in the Hubbard model with repulsion

Abstract

A study has been made, using Green's functions for temperature, of the Hubbard model with repulsive interaction. The existence is demonstrated of an antiferromagnetic state in the case of a half-filled zone. The existence of a superconducting state with p-pairing in the three-dimensional model is shown for low densities of electrons or holes. The highest superconducting transition temperature is reached in a two-dimensional model when the saddle point of the energy function (Van Hove point) is situated on the Fermi surface. The type of superconducting pairing can be called “superposition pairing with odd angular momenta” (to a first approximation this is p-pairing). The problem of competition between superconductivity and ferromagnetism is discussed. It is shown that superconductivity is favored for u/t ≳ 8.