Odd q-state clock spin-glass models in three dimensions, asymmetric phase diagrams, and multiple algebraically ordered phases

Distinctive orderings and phase diagram structures are found, from renormalization-group theory, for odd q-state clock spin-glass models in d = 3 dimensions. These models exhibit asymmetric phase diagrams, as is also the case for quantum Heisenberg spin-glass models. No finite-temperature spin-glass phase occurs. For all odd q >= 5, algebraically ordered antiferromagnetic phases occur. One such phase is dominant and occurs for all q >= 5. Other such phases occupy small low-temperature portions of the phase diagrams and occur for 5 <= q <= 15. All algebraically ordered phases have the same structure, determined by an attractive finite-temperature sink fixed point where a dominant and a subdominant pair states have the only nonzero Boltzmann weights. The phase transition critical exponents quickly saturate to the high q value.