Dynamic critical behavior of the $\mathrm{XY}$ model in small-world networks

The critical behavior of the $\mathrm{XY}$ model on small-world network is investigated by means of dynamic Monte Carlo simulations. We use the short-time relaxation scheme, i.e., the critical behavior is studied from the nonequilibrium relaxation to equilibrium. Static and dynamic critical exponents are extracted through the use of the dynamic finite-size scaling analysis. It is concluded that the dynamic universality class at the transition is of the mean-field nature. We also confirm numerically that the value of dynamic critical exponent is independent of the rewiring probability P for $P\gtrsim \mathrm{0.03.}$