We propose toy models of unconventional magnetic alloys, in which the density of band states, $ρ(ε)$, and hybridization, $t(ε)$, are energy dependent; it is assumed, however, that $t^2(ε)\proptoρ^{-1}(ε)$, and hence an effective electron-impurity coupling $Γ(ε)=ρ(ε)t^2(ε)$ is energy independent. In the renormalization group approach, the physics of the system is assumed to be governed by $Γ(ε)$ only rather than by separate forms of $ρ(ε)$ and $t(ε)$. However, an exact Bethe Ansatz solution of the toy Anderson model demonstrates a crucial role of a form of inverse band dispersion $k(ε)$.

A final version. A previous one has been sent to Archive because of my technical mistake. Sorry