Vacancy mechanism for Ising critical dynamics

A kinetic Ising model with a vacancy mechanism of relaxation is introduced. This model is believed to give a realistic picture of the critical dynamics of binary alloys while existing models do not represent the actual microscopic mechanism of ordering. The initial decay time of the relaxation of the order is calculated exactly and the existence of critical slowing down is proved. A Monte Carlo calculation indicates that although the order parameter and the energy are not conserved quantities, the critical index of the order parameter relaxation ${\Delta }_n$ is different from that of the one-spin-flip kinetic Ising model. In the temperature region $0.074<\mathrm{}\frac{(T-T_c)}{T_c}<1\mathrm{}$, the Monte Carlo estimate yields ${\Delta }_n=\gamma \pm 7\%$, with $\gamma$ being the critical index of the susceptibility. In the same temperature region the nonlinear relaxation time cannot be described by a single exponent.