A study of the 2D Hubbard model in the paramagnetic phase by means
of the *COM* is reported in
Refs. [37,2,38,39,40,41,3,4,42,43,44,45,42]. In particular the following properties have been computed:

- The thermodynamic properties (i.e., chemical potential, double
occupancy, local magnetic moment, internal energy, free energy,
entropy, specific heat)
[37,2,38,4,45]
- The single-particle properties (i.e., energy spectra, spectral
functions, density of states)
[40,41,3,46]
- The response functions (i.e., charge and spin susceptibilities) [39,46,42]
- The optical properties (i.e., Drude weight, optical conductivity) [43,44]

The *COM* results have been compared with the ones
obtained by:

- Numerical techniques (i.e., Exact diagonalization, Lanczos and quantum
Monte Carlo)
[47,48,49,50,51,52,53,54,55,56,57,58]
- Slave boson technique [59]
- Projection techniques [60]

The paramagnetic solution of the two-dimensional Hubbard model has
been widely studied within the *COM*; it would require
too much space to summarize all works. Among the most relevant
results we note the good agreement with the data of numerical
simulation for all local, integrated and thermodynamical
quantities (chemical potential, double occupancy, local magnetic
moment, internal energy, specific heat). It is also worth
mentioning the calculation of the response functions by means of
the Hubbard propagator, in the one-loop approximation, which gives
good agreement with the quantum Monte Carlo results. The
single-particle properties have been also studied by considering
an approximation where the two-site correlations are combined with
the resolvent method. The lower and upper Hubbard subbands have a
three peak structure at half filling. By doping a coherent peak
develops at the Fermi level. The scenario well reproduces the
results of numerical simulation.