Magnetic Properties and Superconductivity in the Two-Dimensional Repulsive Hubbard Model

A new method for estimating the parameter ensuring the fulfillment of the Mermin-Wagner theorem in the strong coupling diagram technique (SCDT) for the two-dimensional Hubbard model is suggested. With the precise parameter value, calculated magnetic quantities are in good agreement with the results of numeric and optical-lattice experiments. Obtained spin and charge vertices are used for investigating superconductivity in the t-U and t-t'-t ''-U Hubbard models in the regime of strong correlations. We found no superconducting transition in the t-U model. In the t-t'-t ''-U model, the transition occurs for the singlet d(x2 - y2) pairing at T-c approximate to 0.016t. The difference between the two models is in the renormalized hopping describing electron motion in SCDT. In the t-U model, it vanishes for momenta (pi, 0), (0, pi) of extrema of the d-wave order parameter, while the hopping is finite in the t-t'-t ''-U model. In the one-band model, there are optimal values of t' and t '' ensuring the highest T-c.