Migdal-type renormalization-group calculation for the kinetic Ising model

We make use of the calculation of Achiam and Kosterlitz and investigate the generalization of the Migdal-type renormalization-group calculation to critical dynamics, by looking at the one- and two-dimensional kinetic Ising model with no conserved magnetization. In the two-dimensional case the dynamical critical index $Z_M\left(\mathrm{magnetic}\mathrm{perturbation}\right)=2.064\mathrm{}$ and $Z_E\left(\mathrm{energylike}\mathrm{perturbation}\right)=1.819\mathrm{}$ for scale factor $\lambda =1\mathrm{}$. $Z_M$ involves the static $\frac{\beta }{\nu }$ exponent, while $Z_E$ involves $\frac{1}{\nu }$, and therefore, it is not surprising that $Z_M$ is closer to the high-temperature expansion results, since $\frac{\beta }{\nu }$ in the Migdal approximation for statics is much closer to the exact value than $\frac{1}{\nu }$. In one dimension we obtain $Z_M=Z_E=2\mathrm{}$, which is the exact result of Glauber.