  The possibility of the superradiant phase transition in polarizable materials
described by the minimal-coupling Hamiltonian with the longitudinal
dipole-dipole interaction is examined. We try to reduce the Hamiltonian into
the Dicke one in homogeneous and infinite case, and discuss the stability of
normal ground state by the formalism of Green function in spatially
inhomogeneous case. The presence of the longitudinal dipole-dipole interaction
does not enable the superradiant phase transition, if the transverse and
longitudinal fields are decoupled. Although the full dipole-dipole interaction
can be eliminated in the electric-dipole gauge in the absence of overlap
between individual atomic dipoles, we cannot reduce the Hamiltonian to the
Dicke one, because the elimination is justified only if all the transverse and
longitudinal fields remain. Even if the transverse and longitudinal fields are
mixed in spatially inhomogeneous systems, the normal ground state is still
stable if the system does not show the superradiant phase transition in the
homogeneous case.
