Phase diagram of the Kondo lattice

We discuss the phase diagram of the Kondo lattice: we generalize to the lattice a method proposed by Yoshimori and Sakurai for the single-impurity Kondo problem; this method transforms the Kondo exchange interaction into a fictitious $s-f$ hybridization, and gives a resonance of width $T_K$ at the Fermi level. We study the Kondo phase and compare its energy with the energy of the magnetic phase. The Kondo state is stable when the exchange interaction is larger than a critical value; this state is insulating when the conduction band is half filled.