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
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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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