Vortex dynamics for two-dimensional XY models

Two-dimensional XY models with resistively shunted junction (RSJ) dynamics and time dependent Ginzburg-Landau (TDGL) dynamics are simulated and it is verified that the vortex response is well described by the Minnhagen phenom enology for both types of dynamics. Evidence is presented supporting that t he dynamical critical exponent z in the low-temperature phase is given by t he scaling prediction (expressed in terms of the Coulomb gas temperature T- CG and the vortex renormalization given by the dielectric constant <(epsilo n)over tilde>) z = 1/<(epsilon)over tilde>T-CG - 2 greater than or equal to 2 both for RSJ and TDGL and that the nonlinear IV exponent a is given by a = z + 1 in the low-temperature phase. The results are discussed and compar ed with the results of other recent papers and the importance of the bounda ry conditions is emphasized. [S0163-1829(99)05317-5].