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 TK≈Δexp(πEd*2Δ).