Monte Carlo Investigation of Dynamic Critical Phenomena in the Two-Dimensional Kinetic Ising Model

Extending the Monte Carlo method to dynamic critical phenomena we investigated the time-dependent correlation functions in the two-dimensional one-spin-flip Ising model and the critical behavior of the associated relaxation times. These relaxation times are the following: _^, characterizing the approach of the order parameter to equilibrium after a change of temperature of the system; _ and _^A characterizing the slowing down of the order-parameter correlation and autocorrelation functions, respectively; _ and _^A, characterizing the slowing down of the energy correlation and autocorrelation functions; and finally _, characterizing the cross-correlation function. We give estimates for the associated exponents _^___1. 900. 10, and _^A1. 600. 10, _^A0. 950. 10, _^A0, which are consistent with the dynamic scaling hypothesis and with exact inequalities. A detailed comparison with recent high-temperature-expansion estimates is performed, and the reliability of the Monte Carlo results is carefully analyzed.