  We present a study of systems of single-molecule magnets using a
semiclassical analysis and catastrophe theory. Separatrices in parameter space
are constructed which are useful to determine the structure of the Hamiltonians
energy levels. In particular the Maxwell set separatrix determines the behavior
of the ground state of the system. We consider an external magnetic field with
two components, one parallel to the easy magnetization axis of the molecule and
the other perpendicular to it. Using the fidelity and heat capacity we were
able to detect the signals of the QPTs as a function of the magnetic field
components.
