  The effect of a fermion with angular momentum j on quantum phase transitions
of a (s,d) bosonic system is investigated. It is shown that the presence of a
fermion strongly modifies the critical value at which the transition occurs,
and its nature, even for small and moderate values of the coupling constant.
The analogy with a bosonic system in an external field is mentioned.
Experimental evidence for precursors of quantum phase transitions in bosonic
systems plus a fermion (odd-even nuclei) is presented.
