  The spin-3/2 Ising model, with nearest-neighbor interactions only, is the
prototypical system with two different ordering species, with concentrations
regulated by a chemical potential. Its global phase diagram, obtained in d=3 by
renormalization-group theory in the Migdal-Kadanoff approximation or
equivalently as an exact solution of a d=3 hierarchical lattice, with flows
subtended by 40 different fixed points, presents a very rich structure
containing eight different ordered and disordered phases, with more than
fourteen different types of phase diagrams in temperature and chemical
potential. It exhibits phases with orientational and/or positional order. It
also exhibits quintuple phase transition reentrances. Universality of critical
exponents is conserved across different renormalization-group flow basins, via
redundant fixed points. One of the phase diagrams contains a plastic crystal
sequence, with positional and orientational ordering encountered consecutively
as temperature is lowered. The global phase diagram also contains double
critical points, first-order and critical lines between two ordered phases,
critical endpoints, usual and unusual (inverted) bicritical points, tricritical
points, multiple tetracritical points, and zero-temperature criticality and
bicriticality. The 4-state Potts permutation-symmetric subspace is contained in
this model.
