Abstract
We present a study on systems of single-molecule magnet systems using semiclassical analysis and catastrophe theory. Separatrices in the parameter space are constructed, which are useful for determining the structure of the Hamiltonian energy levels. In particular the Maxwell set separatrix determines the behaviour of the ground state of the system. We consider an external magnetic field with two components: one parallel to the easy magnetisation axis of the molecule and the other perpendicular to it. Using fidelity and heat capacity we were able to detect the signals of the quantum phase transitions as a function of the magnetic field components.
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