  The left-right chiral and ferromagnetic-antiferromagnetic double spin-glass
clock model, with the crucially even number of states q=4 and in three
dimensions d=3, has been studied by renormalization-group theory. We find, for
the first time to our knowledge, four different spin-glass phases, including
conventional, chiral, and quadrupolar spin-glass phases, and phase transitions
between spin-glass phases. The chaoses, in the different spin-glass phases and
in the phase transitions of the spin-glass phases with the other spin-glass
phases, with the non-spin-glass ordered phases, and with the disordered phase,
are determined and quantified by Lyapunov exponents. It is seen that the chiral
spin-glass phase is the most chaotic spin-glass phase. The calculated phase
diagram is also otherwise very rich, including regular and temperature-inverted
devil's staircases and reentrances.
