Geometrical structure and critical phenomena in the fermion dynamical symmetry model: Sp(6)

A description of the intrinsic (geometrical) structure of the Sp(6) fermion dynamical symmetry model is presented using the coherent state method. A detailed analytical study of the critical behavior of this model is given for the intrinsic ground state as a function of the fundamental control parameter: the valence particle number. The results show that the effect of the Pauli principle is to limit the deformation and to cause a transition from axial to triaxial symmetry.