Journal of Statistical Physics

, Volume 161, Issue 5, pp 1231–1235 | Cite as

Kondo Effect in the Hierarchical \(s-d\) Model

  • Giovanni Gallavotti
  • Ian JauslinEmail author


The \(s-d\) model describes a chain of spin-1/2 electrons interacting magnetically with a two-level impurity. It was introduced to study the Kondo effect, in which the magnetic susceptibility of the impurity remains finite in the 0-temperature limit as long as the interaction of the impurity with the electrons is anti-ferromagnetic. A variant of this model was introduced by Andrei, which he proved was exactly solvable via Bethe Ansatz. A hierarchical version of Andrei’s model was studied by Benfatto and the authors. In the present letter, that discussion is extended to a hierarchical version of the \(s-d\) model. The resulting analysis is very similar to the hierarchical Andrei model, though the result is slightly simpler.


Renormalization group Non-perturbative renormalization Kondo effect Fermionic hierarchical model Quantum field theory 



We are grateful to G. Benfatto for many enlightening discussions on the \(s-d\) and Andrei’s models.


  1. 1.
    Anderson, P.: Local magnetized states in metals. Phys. Rev. 124, 41–53 (1961)MathSciNetCrossRefADSGoogle Scholar
  2. 2.
    Andrei, N.: Diagonalization of the Kondo Hamiltonian. Phys. Rev. Lett. 45, 379–382 (1980)CrossRefADSGoogle Scholar
  3. 3.
    Benfatto, G., Gallavotti, G., Jauslin, I.: Kondo effect in a fermionic hierarchical model. arXiv:1506.04381 (2015)
  4. 4.
    Kondo, J.: Resistance minimum in dilute magnetic alloys. Prog. Theor. Phys. 32, 37–49 (1964)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.INFN-Roma1 and Rutgers UniversityRomeItaly
  2. 2.Dipartimento di FisicaUniversity of Rome “La Sapienza”RomeItaly

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