  The series of articles [Ann. Phys. 345, 73 (2014) and 356, 57 (2015)] devoted
to excited-state quantum phase transitions (ESQPTs) in systems with $f=2$
degrees of freedom is continued by studying the interacting boson model of
nuclear collective dynamics as an example of a truly many-body system. The
intrinsic Hamiltonian formalism with angular momentum fixed to $L=0$ is used to
produce a generic first-order ground-state quantum phase transition with an
adjustable energy barrier between the competing equilibrium configurations. The
associated ESQPTs are shown to result from various classical stationary points
of the model Hamiltonian, whose analysis is more complex than in previous cases
because of (i) a non-trivial decomposition to kinetic and potential energy
terms and (ii) the boundedness of the associated classical phase space.
Finite-size effects resulting from a partial separability of both degrees of
freedom are analyzed. The features studied here are inherent in a great
majority of interacting boson systems.
