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: ${\tau }_{\delta \mu }^{\Delta T}$, characterizing the approach of the order parameter to equilibrium after a change of temperature $\Delta T$ of the system; ${\tau }_{\delta \mu \delta \mu }$ and ${\tau }_{\delta \mu \delta \mu }^A$ characterizing the slowing down of the order-parameter correlation and autocorrelation functions, respectively; ${\tau }_{\delta \mathcal{H}\delta \mathcal{H}}$ and ${\tau }_{\delta \mathcal{H}\delta \mathcal{H}}^A$, characterizing the slowing down of the energy correlation and autocorrelation functions; and finally ${\tau }_{\delta \mu \delta \mathcal{H}}$, characterizing the cross-correlation function. We give estimates for the associated exponents ${\Delta }_{\delta \mu }^{\Delta T}\approx {\Delta }_{\delta \mu \delta \mu }\approx {\Delta }_{\delta \mathcal{H}\delta \mathcal{H}}\approx {\Delta }_{\delta \mu \delta \mathcal{H}}\approx 1.90\pm 0.10$, and ${\Delta }_{\delta \mu \delta \mu }^A\approx 1.60\pm 0.10$, ${\Delta }_{\delta \mu \delta \mathcal{H}}^A\approx 0.95\pm 0.10$, ${\Delta }_{\delta \mathcal{H}\delta \mathcal{H}}^A\approx 0$, 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.