$\frac{1}{N}$ expansion for the Kondo lattice

A diagrammatic expansion is developed for the partition function of a lattice of spin-$j$ local moments interacting with a band via the Coqblin-Schrieffer exchange interaction. By examining the limit of large spin degeneracy, $N=2j+1\mathrm{}$, a $\frac{1}{N}$ expansion is obtained for the partition function, which clearly exhibits how local spin fluctuations are enhanced by large spin degeneracy. The competition between the Ruderman-Kittel-Kasuya-Yosida interaction and local Kondo spin fluctuations is examined using scaling theory, and the critical value of the Kondo coupling constant above which a spin-compensated Kondo-lattice ground state is stable is shown to tend to zero as $O\left(\frac{1}{N}\right)$, providing new justification for the applicability of the Kondo-lattice model to rare-earth systems. Physical arguments are advanced, based on the nature of the crossover to the strong-coupling regime, which suggest that the low-temperature excitations of the Kondo lattice form a narrow band of heavy fermions.