A thermodynamic description of the Mott-Hubbard transition

An effective one-particle spectrum has been derived for up-spins in the presence of static down-spins, with which they interact through a repulsive Hubbard term. This is done by finding the stable thermodynamic limit of the partition function, and expanding it around the overdoped limit. The effective model is purely fermionic, without slave fields. In the three-band case, an in-gap band appears for the up-spins, with the chemical potential moving into the charge transfer gap already before half-filling. Due to the precise treatment of disorder, avoiding any averaging of the occupation number of the electrons at a given site, the entropy is a non-trivial function of doping, despite a k-space formulation and the in-gap fermions having a large Fermi surface