Abstract
The concept of supersymmetry and phase transitions are brought together through a study of the consistent-$Q$ Hamiltonian of the interacting Boson-Fermion model, constructed with a vibrational one-body term and a quadrupole-quadrupole interaction, and which is applicable to odd-$A$ nuclei with dominant $j=\frac{1}{2}$, $\frac{3}{2}$, and $\frac{5}{2}$ single-particle orbits. A conservation condition for the pseudo-orbital angular momentum is discussed.
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