Current-voltage characteristics of the two-dimensional $\mathrm{XY}$ model with Monte Carlo dynamics

Current-voltage characteristics and the linear resistance of the two-dimensional $\mathrm{XY}$ model with and without external uniform current driving are studied by Monte Carlo simulations. We apply the standard finite-size scaling analysis to get the dynamic critical exponent z at various temperatures. From the comparison with the resistively shunted junction dynamics, it is concluded that z is universal in the sense that it does not depend on details of dynamics. This comparison also leads to the quantification of the time in the Monte Carlo dynamic simulation.