Magnetic field effects in the Anderson model of dilute magnetic alloys. I. Self-consistent solution

We have studied the infinite-$U$ Anderson dilute-alloy model in arbitrary magnetic fields by means of the double-time Green's-function method. Using a truncation procedure, the coupled equations are reduced to a singular integral equation for the transition matrix. The integral equation is then solved exactly by analytic methods. The impurity-electron occupation number $〈n〉$ is calculated for general values of parameters, $\Delta$, ${\epsilon }_d$, and $T$ at zero field. It is found that the local moment exhibits strong temperature dependence at temperatures above the Kondo temperature.