Dynamic critical behavior of the one-dimensional XY model with a long-range interaction.

We numerically study dynamic critical behavior of the one-dimensional XY model with a long-range interaction by using the Monte Carlo method and the resistively-shunted Josephson junction model. The two dynamic models exhibit the mean-field universality class in equilibrium as expected, but the dynamic critical behavior is shown to sensitively depend on details of numerical simulation. In more detail, the trial angle range in the Monte Carlo simulation is found to alter the value of the dynamic critical exponent, and the scaling of the Monte Carlo time unit by the acceptance ratio is shown to be useful to improve the estimation of the dynamic critical exponent. We compare the Monte Carlo result of the dynamic critical exponent with the result from the more realistic dynamic model of the resistively-shunted junction. We conclude that the small value of the trial angle range should be used to properly detect dynamic critical behavior. [ABSTRACT FROM AUTHOR]