  A spin system is studied, with simultaneous permutation-symmetric Potts and
spin-rotation-symmetric clock interactions, in spatial dimensions d=2 and 3.
The global phase diagram is calculated from the renormalizaton-group solution
with the recently improved (spontaneous first-order detecting) Migdal-Kadanoff
approximation or, equivalently, with hierarchical lattices with the inclusion
of effective vacancies. Five different ordered phases are found: conventionally
ordered ferromagnetic, quadrupolar, antiferromagnetic phases and algebraically
ordered antiferromagnetic, antiquadrupolar phases. These five different ordered
phases and the disordered phase are mutually bounded by first- and second-order
phase transitions, themselves delimited by multicritical points: inverted
bicritical, zero-temperature bicritical, tricritical, second-order bifurcation,
and zero-temperature highly degenerate multicritical points. One rich phase
diagram topology exhibits all of these phenomena.
