Critical dynamics of kinetic Ising models in four dimensions

The effective kinetic coefficient of a kinetic Ising model with a nonconserved order parameter coupled to a conserved energy field in four dimensions varies as ${\left|\ln \right(T-T_c\left)\right|}^{\sigma }$ with $-\frac{2}{3}<~\sigma <~0$. These results should apply to dipolar Ising systems in three dimensions whose dynamics are purely relaxational, although it is very difficult to find the exact value of $\sigma$.