  Antiferromagnetic heavy fermion metals close to their quantum critical points
display a richness in their physical properties unanticipated by the
traditional approach to quantum criticality, which describes the critical
properties solely in terms of fluctuations of the order parameter. This has led
to the question as to how the Kondo effect gets destroyed as the system
undergoes a phase change. In one approach to the problem, Kondo lattice systems
are studied through a self-consistent Bose-Fermi Kondo model within the
Extended Dynamical Mean Field Theory. The quantum phase transition of the Kondo
lattice is thus mapped onto that of a sub-Ohmic Bose-Fermi Kondo model. In the
present article we address some aspects of the failure of the standard
order-parameter functional for the the Kondo-destroying quantum critical point
of the Bose-Fermi Kondo model.
