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Exact Results in the Kondo Problem. II. Scaling Theory, Qualitatively Correct Solution, and Some New Results on One-Dimensional Classical Statistical Models

1970; American Physical Society; Volume: 1; Issue: 11 Linguagem: Inglês

10.1103/physrevb.1.4464

0556-2805

Philip W. Anderson, G. Yuval, D. R. Hamann,

Markov Chains and Monte Carlo Methods

The simplest Kondo problem is treated exactly in the ferromagnetic case, and given exact bounds for the relevant physical properties in the antiferromagnetic case, by use of a scaling technique on an asymptotically exact expression for the ground-state properties given earlier. The theory also solves the $n=2$ case of the one-dimensional Ising problem. The ferromagnetic case has a finite spin, while the antiferromagnetic case has no truly singular $T\ensuremath{\rightarrow}0$ properties (e.g., it has finite $\ensuremath{\chi}$).