  Earlier work on dynamical critical phenomena in the context of magnetic
hysteresis for uniaxial (scalar) spins, is extended to the case of a
multicomponent (vector) field. From symmetry arguments and a perturbative
renormalization group approach (in the path integral formalism), it is found
that the generic behavior at long time and length scales is described by the
scalar fixed point (reached for a given value of the magnetic field and of the
quenched disorder), with the corresponding Ising-like exponents. By tuning an
additional parameter, however, a fully rotationally invariant fixed point can
be reached, at which all components become critical simultaneously, with
O(n)-like exponents. Furthermore, the possibility of a spontaneous
non-equilibrium transverse ordering, controlled by a distinct fixed point, is
unveiled and the associated exponents calculated. In addition to these central
results, a didactic ``derivation'' of the equations of motion for the spin
field are given, the scalar model is revisited and treated in a more direct
fashion, and some issues pertaining to time dependences and the problem of
multiple solutions within the path integral formalism are clarified.
