Journal of Statistical Physics

, Volume 161, Issue 5, pp 1203–1230 | Cite as

Kondo Effect in a Fermionic Hierarchical Model

  • Giuseppe Benfatto
  • Giovanni Gallavotti
  • Ian JauslinEmail author


In this paper, a fermionic hierarchical model is defined, inspired by the Kondo model, which describes a 1-dimensional lattice gas of spin-1/2 electrons interacting with a spin-1/2 impurity. This model is proved to be exactly solvable, and is shown to exhibit a Kondo effect, i.e. that, if the interaction between the impurity and the electrons is antiferromagnetic, then the magnetic susceptibility of the impurity is finite in the 0-temperature limit, whereas it diverges if the interaction is ferromagnetic. Such an effect is therefore inherently non-perturbative. This difficulty is overcome by using the exact solvability of the model, which follows both from its fermionic and hierarchical nature.


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



We are grateful to V. Mastropietro for suggesting the problem and to A. Giuliani, V. Mastropietro and R. Greenblatt for continued discussions and suggestions, as well as to J. Lebowitz for hospitality and support.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Giuseppe Benfatto
    • 1
  • Giovanni Gallavotti
    • 2
  • Ian Jauslin
    • 3
    Email author
  1. 1.Università degli studi di Roma “Tor Vergata”RomaItaly
  2. 2.INFN-Roma1 and Rutgers UniversityRomaItaly
  3. 3.Dipartimento di FisicaUniversity of Rome “La Sapienza”RomaItaly

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