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Distinctive orderings and phase diagram structures are found, fromrenormalization-group theory, for odd q-state clock spin-glass models in d=3dimensions. These models exhibit asymmetric phase diagrams, as is also the casefor quantum Heisenberg spin-glass models. No finite-temperature spin-glassphase occurs. For all odd $q\geqslant 5$, algebraically orderedantiferromagnetic phases occur. One such phase is dominant and occurs for all$q\geqslant 5$. Other such phases occupy small low-temperature portions of thephase diagrams and occur for $5 \leqslant q \leqslant 15$. All algebraicallyordered phases have the same structure, determined by an attractivefinite-temperature sink fixed point where a dominant and a subdominant pairstates have the only non-zero Boltzmann weights. The phase transition criticalexponents quickly saturate to the high q value.

Odd q-State Clock Spin-Glass Models in Three Dimensions, Asymmetric Phase Diagrams, and Multiple Algebraically Ordered Phases