  We investigate the ordering kinetics for axial next nearest neighbor Ising
(ANNNI) model in one and two dimensions by the multi-spin heat bath dynamical
simulation. This dynamics enables us to overcome the pinning effect and to
observe the dynamical scaling law for domain growth in the ANNNI model at zero
temperature. The domain growth exponent is 1/2 isotropically both in the
ferromagnetic and the dry-(commensurate) antiphase. In the wet-(commensurate)
antiphase, however, it is approximately 1/3 in the modulated direction, whereas
it remains 1/2 in the non-modulated direction. We suggest that these exponent
values are dictated by 3 and 4 body diffusion-reaction processes of domain
walls.
