Scaling theory of the asymmetric Anderson model

A scaling theory is used to show that for temperatures TU, the properties of the asymmetric Anderson model (U|Ed|,Δ) are universal functions of the scaling invariants Δ and Ed*=Ed+(Δπ)ln(W0Δ), where W0 is the conduction electron bandwidth or U, whichever is smaller. Crossovers between various regimes of simple behavior as the temperature changes are described. |Ed*|Δ is identified as the criterion for a "mixed-valence" ground state, where the susceptibility Δ-1. For -Ed*Δ, there is a local-moment regime with a Kondo temperature TKΔexp(πEd*2Δ).