Functional integral approach to the static susceptibility of the Anderson model

The author considers the Anderson model for dilute magnetic alloys and uses the functional integral approach to calculate the static susceptibility. The Coulomb interaction at the magnetic impurity is represented by the random fields coupled to the charge and the spin fluctuations. On treating the charge fluctuations within the extremal approximation, the free-energy functional is approximated by its potential part plus the harmonic terms in its kinetic part. Within this approximation, the functional integral is evaluated over all the paths by using the transfer matrix technique. The static susceptibility reduces to an expression of a system of independent particles moving in a one-dimensional potential. In the weak-coupling limit (U/πδ <1, U is the Coulomb interaction at the impurity and δ is the width of its virtually bound d-state), it behaves like the Pauli susceptibility and coincides with perturbation theory results, up to first order in U/πδ. In strong-coupling limits (U/πδ > 1), at low temperatures, it shows the tendency to saturation (Kondo effect) and, at high temperatures, behaves like a Curie susceptibility and coincides with the perturbation results, up to first order in πδ/U. (author)