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The condensation energy and the specific heat jump of a two-dimensionalHubbard model, suitable to discuss high-$T_c$ superconductors, is studied. Inthis work, the Hubbard model is investigated by the Green's function methodwithin a $n$-pole approximation, which allows to consider superconductivitywith $d_{x^2-y^2}$-wave pairing. In the present scenario, the pseudogap regimeemerges when the antiferromagnetic (AF) correlations become sufficiently strongto move to lower energies the region around of the nodal point $(\pi,\pi)$ onthe renormalized bands. It is observed that above a given total occupation$n_T$, the specific heat jump $\Delta C$ and also the condensation energy$U(0)$ decrease signaling the presence of the pseudogap.

Interplay between condensation energy, pseudogap and the specific heat of a Hubbard model in a n-pole approximation