Critical hysteresis for n-component magnets

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 nonequilibrium 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 diner fashion, and some issues pertaining to time dependences and the problem of multiple solutions within the path-integral formalism are clarified.