THE DYNAMIC CRITICAL EXPONENT OF THE 2-DIMENSIONAL, 3-DIMENSIONAL AND 5-DIMENSIONAL KINETIC ISING-MODEL

We present Monte Carlo simulation results for the dynamical critical exponent z of the two-, three- and five-dimensional kinetic Ising model. We used Glauber as well as Metropolis dynamics. Both type of dynamics lead to the same z-values in two and three dimensions. The z-values were calculated from the magnetization relaxation from an ordered state into the equilibrium state at T(c) for very large systems (up to (169984)2, (3072)3 and (48)5). For the two-dimensional case we obtain z = 2.21 +/- 0.03 and for the three-dimensional case z = 2.08 +/- 0.03. For the five-dimensional Glauber case, the requirement z = 2 gives a critical point J/k(B)T(c) = 0.11391 from Monte Carlo simulations, whereas new series expansions with four more terms give 0.113935 +/- 0.000015 for this ratio.