Nematic phase of the n-component cubic-spin spin glass in d=3: Liquid-crystal phase in a dirty magnet

A nematic phase, previously seen in the n= 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 components n >= 3, in spatial dimension n= 3, thus constituting a liquid-crystal phase in a dirty (quenched-disordered) magnet. This result is obtained from renormalization-group calculations that are exact on the hierarchical lattice and, equivalently, approximate on the cubic spatial lattice. The nematic phase completely intervenes between the spin-glass phase and the disordered phase. The Lyapunov exponents of the spin-glass chaos are calculated from n= 1 up to n= 12 and show odd-even oscillations with respect to n.