Dynamical universality classes of the superconducting phase transition

We present a finite temperature Monte Carlo study of the XY model in the vortex representation and study its dynamical critical behavior in two limits. The first neglects magnetic-field fluctuations, corresponding to the absence of screening, which should be a good approximation in high-T-c superconductors (kappa-->infinity) except extremely close to the critical point. Here, from finite-size scaling of the linear resistivity we find the dynamical critical exponent of the vortex motion to be z approximate to 1.5. The second limit includes magnetic-field fluctuations in the strong screening limit (kappa-->0) corresponding to the true asymptotic inverted XY critical regime, when we find the unexpectedly large value z approximate to 2.7. We compare these results, obtained from dissipative dynamics in the vortex representation, with the universality class of the corresponding model in the phase representation with propagating (spin-wave) modes. We also discuss the effect of disorder and the relevance of our results for experiments.