ABSTRACT
A scaling theory is used to show mat for temperatures T ≪ U, me properties of the asymmetric Anderson model ( U ≫ | E d | , Δ ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429494116/afa305c7-7e11-4618-94aa-661e4acf5b1d/content/eq2646.tif"/> are universal functions of the scaling invariants Δ and E d * = E d + ( Δ / π ) ln ( W 0 / Δ ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429494116/afa305c7-7e11-4618-94aa-661e4acf5b1d/content/eq2647.tif"/> , where W 0 is the conduction electron bandwidth or U, whichever is smaller. Crossovers between various regimes of simple behavior asthe temperature changes are described. | E d * | < ˜ Δ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429494116/afa305c7-7e11-4618-94aa-661e4acf5b1d/content/eq2648.tif"/> is identified as the criterion for a “mixed-valence” ground state, where the susceptibility ≈ Δ−1. For − E d * ≫ Δ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429494116/afa305c7-7e11-4618-94aa-661e4acf5b1d/content/eq2649.tif"/> , there is a local-moment regime with a Kondo temperature T K ≈ Δ exp ( π E d * / 2 Δ ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429494116/afa305c7-7e11-4618-94aa-661e4acf5b1d/content/eq2650.tif"/> ).
