**Authors**
: Giuseppe Benfatto, Giovanni Gallavotti, Ian Jauslin

**Title:** *
Kondo effect in a fermionic hierarchical model
*

**Sommario**:*
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.
*

**Keywords**:
Renormalization group; Non-perturbative renormalization;
Kondo effect; Fermionic hierarchical model; Quantum field theory

Giuseppe Benfatto

Università degli studi di Roma "Tor Vergata", 00133 Roma, Italy

benfatto@mat.uniroma2.it

Giovanni Gallavotti

INFN Fisica, Rutgers University e Accademia dei Lincei

Università di Roma Sapienza, 00185 Roma, Italy

giovanni.gallavotti@roma1.infn.it

Ian Jauslin

University of Rome "La Sapienza", 00185 Roma, Italy

ian.jauslin@roma1.infn.it

http://ian.jauslin.org

**Supplementary material**:
The computation of the flow equation for the hierarchical Kondo
model can be carried out using the
meankondo
program, available from
http://ian.jauslin.org/software/meankondo