Interplay between condensation energy, pseudogap and the specific heat   of a Hubbard model in a n-pole approximation
  The condensation energy and the specific heat jump of a two-dimensional Hubbard model, suitable to discuss high-$T_c$ superconductors, is studied. In this work, the Hubbard model is investigated by the Green's function method within a $n$-pole approximation, which allows to consider superconductivity with $d_{x^2-y^2}$-wave pairing. In the present scenario, the pseudogap regime emerges when the antiferromagnetic (AF) correlations become sufficiently strong to move to lower energies the region around of the nodal point $(\pi,\pi)$ on the 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. 
A. C. Lausmann, E. J. Calegari, S. G. Magalhaes, C. M. Chaves and A.   Troper
cond-mat.str-el cond-mat.supr-con