  The case of U(5)--$\hat{Q}(\chi)\cdot\hat{Q}(\chi)$ mixing in the
configuration-mixed Interacting Boson Model is studied in its mean-field
approximation. Phase diagrams with analytical and numerical solutions are
constructed and discussed. Indications for first-order and second-order shape
phase transitions can be obtained from binding energies and from critical
exponents, respectively.
