  We study the ground state and classify its phase diagram for a mixture of two
spin-1 condensates in the absence of external magnetic (B-) field according to
atomic parameters for intra- and inter-species spin exchange coupling and
singlet pairing interaction. Ignoring the inter-species singlet pairing
interaction, the ground state phases are found analytically. Numerical approach
of simulated annealing is adopted when the singlet pairing interaction is
present. Our results on the phase diagram and the boundaries between phases
allow for easy identifications of quantum phase transitions, that can be
induced through the tuning of optical traps and atom numbers. They provide the
first insight and guidance for several ongoing experiments on mixtures of
spinor condensates.
