  Using the synchronization mechanism developed in the previous work on the
Potts spin glass model, arXiv:1512.00370, we obtain the analogue of the Parisi
formula for the free energy in the mixed even $p$-spin models with vector
spins, which include the Sherrington-Kirkpatrick model with vector spins
interacting through their scalar product. As a special case, this also
establishes the sharpness of Talagrand's upper bound for the free energy of
multiple mixed $p$-spin systems coupled by constraining their overlaps.
