  We study the XX model for quantum spins on the star graph with three legs
(i.e., on a Y-junction). By performing a Jordan-Wigner transformation
supplemented by the introduction of an auxiliary space we find a Kondo
Hamiltonian of fermions, in the spin 1 representation of su(2), locally coupled
with a magnetic impurity. In the continuum limit our model is shown to be
equivalent to the 4-channel Kondo model coupling spin-1/2 fermions with a
spin-1/2 impurity and exhibiting a non-Fermi liquid behavior. We also show that
it is possible to find a XY model such that - after the Jordan-Wigner
transformation - one obtains a quadratic fermionic Hamiltonian directly
diagonalizable.
