Axial, planar-diagonal, body-diagonal fields on the cubic-spin spin glass in d=3: A plethora of ordered phases under finite fields

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 $n\ge 3$, 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 is found. Under uniform magnetic fields, 17 different phases and two spin-glass phase diagram topologies (meaning the occurrences and relative positions of the many phases), 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 $d=3$ hierarchical lattice and, equivalently, approximate on the cubic 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 $d=3$.