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 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. 
Rava da Silveira and Mehran Kardar