Scaling analysis of a model Hamiltonian for Ce impurity in a cubic metal

We introduce various exchange interactions in a model Hamiltonian for Ce3+ ions in cubic symmetry with three configurations (f0,f1,f2). With the impurity pseudo spin SI = 1/2, our Hamiltonian includes: (i) One-channel Sc = 1/2 Anderson model; (ii) Two-channel Sc = 1/2 Anderson model; (iii) An unforseen one-channel Sc = 3/2 Anderson model with a non-trivial fixed point; (iv) Mixing exchange interaction between the Γ6,7 and the Γ8 conduction electron partial wave states; (v) Multiple conduction electron partial wave states. Using the third-order scaling (perturbative renormalization group) analysis, we study stability of various fixed points relevant to various exchange interactions for Ce3+ ions in cubic symmetry.