Kondo lattice: Renormalization study using a new pseudofermion representation

A new field-theory method for spin $\frac{1}{2}$ is developed using the Berezin and Marinov pathintegral formalism. This method does not have the usual troubles of Abrikosov's pseudofermion representation. In particular, the linked graph theorem is valid. This method is then applied to the study of the Kondo lattice. In the disordered state the effective coupling satisfies the usual renormalization-group equation for the Kondo problem. In the ferromagnetic state it displays the competition between Kondo effect and magnetic ordering. Using the first-order renormalization-group equation, Doniach's criterion based on comparison of the binding energies of the Kondo singlet and the Ruderman-Kittel-Yosida ferromagnetic state is recovered. In second order the feedback from the Kondo effect on the magnetization enhances the Kondo effect and suppresses magnetic order.