## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 1203-1230 |

Number of pages | 28 |

Journal | Journal of Statistical Physics |

Volume | 161 |

Issue number | 5 |

DOIs | |

State | Published - Dec 1 2015 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

## Keywords

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