  We investigate the equilibrium behaviour of a superconducting circuit QED
system containing a large number of artificial atoms. It is shown that the
currently accepted standard description of circuit QED via an effective model
fails in an important aspect: it predicts the possibility of a superradiant
quantum phase transition, even though a full microscopic treatment reveals that
a no-go theorem for such phase transitions known from cavity QED applies to
circuit QED systems as well. We generalize the no-go theorem to the case of
(artificial) atoms with many energy levels and thus make it more applicable for
realistic cavity or circuit QED systems.
