  A nematic phase, previously seen in the d=3 classical Heisenberg spin-glass
system, occurs in the n-component cubic-spin spin-glass system, between the
low-temperature spin-glass phase and the high-temperature disordered phase, for
number of spin components n>=3, in spatial dimension d=3, thus constituting a
liquid-crystal phase in a dirty (quenched-disordered) magnet. Furthermore,
under application of a variety of uniform magnetic fields, a veritable plethora
of phases are found. Under uniform magnetic fields, 15 different phases and two
spin-glass phase diagram topologies, qualitatively different from the
conventional spin-glass phase diagram topology, are seen. The chaotic rescaling
behaviors and their Lyapunov exponents are calculated in each of these
spin-glass phase diagram topologies. These results are obtained from
renormalization-group calculations that are exact on the hierarchical lattice
and, equivalently, approximate on the hypercubic spatial lattice. Axial,
planar-diagonal, or body-diagonal finite-strength uniform fields are applied to
n=2 and 3 component cubic-spin spin-glass systems in d=3.
