A study of the 2D Hubbard model in the superconducting phase by
means of the *COM* is reported in
Refs. [67,68,69]. In
particular the following properties have been computed:

- The thermodynamic properties (i.e., critical temperature, order
parameters, phase symmetry, superconducting gap, internal energy)
[67,68,69]
- The single-particle properties (i.e., energy spectra) [69]

The *COM* results have been analyzed in relation with
the ones obtained by:

By considering singlet pairing in the s- and d- wave channels it has been shown that the two-dimensional Hubbard model supports both solutions. By considering the free energy and the order parameter, we have studied [67,68] the phase diagrams in the three dimensional space (, , ), For both pairing states the solution exists only in a narrow region of ; a relatively strong potential (say ) inhibits the pairing. The s-wave solution exists in a wide range of filling and temperature, not compatible with the range experimentally observed. On the contrary, the phase diagram of the d-wave solution is quantitatively very close to the experimental one, with superconductivity strongly enhanced by the van Hove singularity. The momentum dependence of the gap function along the Fermi surface, studied in Ref. [69], reflects the d-wave symmetry of the order parameter.