Intermediate time scaling in classical continuous-spin models

The time-dependent total spin correlation functions of the two- and the thr ee-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 f ound in our previous work is re-examined. By introducing a phenomenological characteristic time for this intermediate time interval, the second dynami c scaling behavior can be explained. Moreover, the dynamic critical exponen t found from this novel characteristic time is found to be identical to tha t found from the usual dynamic scaling theory developed in the wave vector and frequency domain. For continuous spin models, in which the spin variabl e related to a long-range order parameter is not a constant of motion, our method yielded the dynamic critical exponent with less computational effort s.