Intermediate time scaling in classical continuous-spin models

The time-dependent total spin correlation functions of the two- and the three-dimensional classical XY models seem to have a very narrow first dynamic scaling interval and, after this interval, a much broader anomalous second dynamic scaling interval appears. In this paper, this intriguing feature found in our previous work is re-examined. By introducing a phenomenological characteristic time for this intermediate time interval, the second dynamic scaling behavior can be explained. Moreover, the dynamic critical exponent found from this novel characteristic time is found to be identical to that found from the usual dynamic scaling theory developed in the wave vector and frequency domain. For continuous spin models, in which the spin variable related to a long-range order parameter is not a constant of motion, our method yielded the dynamic critical exponent with less computational efforts