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: τ_δμ^ΔT, characterizing the approach of the order parameter to equilibrium after a change of temperature ΔT of the system; τ_δμδμ and τ_δμδμA characterizing the slowing down of the order-parameter correlation and autocorrelation functions, respectively; τ_δHδH and τ_δHδHA, characterizing the slowing down of the energy correlation and autocorrelation functions; and finally τ_δμδH, characterizing the cross-correlation function. We give estimates for the associated exponents ${{Δ}}_{{δ}{μ}}^{{Δ}T}{≈}{{Δ}}_{{δ}{μ}{δ}{μ}}{≈}{{Δ}}_{{δ}H{δ}H}{≈}{{Δ}}_{{δ}{μ}{δ}H}{≈}1.90±{}0.10$, and ${{Δ}}_{{δ}{μ}{δ}{μ}}A{≈}1.60±{}0.10$, ${{Δ}}_{{δ}{μ}{δ}H}A{≈}0.95±{}0.10$, ${{Δ}}_{{δ}H{δ}H}A{≈}0$, 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.