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Spin-glass phases and phase transitions for q-state clock models and their q$\rightarrow \infty$ limit the XY model, in spatial dimension d=3, are studiedby a detailed renormalization-group study that is exact for the d=3hierarchical lattice and approximate for the cubic lattice. In addition to thenow well-established chaotic rescaling behavior of the spin-glass phase, eachof the two types of spin-glass phase boundaries displays, underrenormalization-group trajectories, their own distinctive chaotic behavior.These chaotic renormalization-group trajectories subdivide into two categories,namely as strong-coupling chaos (in the spin-glass phase and, distinctly, onthe spinglass-ferromagnetic phase boundary) and as intermediate-coupling chaos(on the spinglass-paramagnetic phase boundary). We thus characterize eachdifferent phase and phase boundary exhibiting chaos by its distinct Lyapunovexponent, which we calculate. We show that, under renormalization-group,chaotic trajectories and fixed distributions are mechanistically andquantitatively equivalent. The phase diagrams of arbitrary even q-state clockspin-glass models in d=3 are calculated. These models, for all non-infinite q,have a finite-temperature spin-glass phase. Furthermore, the spin-glass phasesexhibit a universal ordering behavior, independent of q. The spin-glass phasesand the spinglass-paramagnetic phase boundaries exhibit universal fixeddistributions, chaotic trajectories and Lyapunov exponents. In the XY modellimit, our calculations indicate a zero-temperature spin-glass phase.

High q-State Clock Spin Glasses in Three Dimensions and the Lyapunov Exponents of Chaotic Phases and Chaotic Phase Boundaries