Anisotropic domain growth of the axial next-nearest-neighbor Ising model at low temperatures

We investigate the ordering kinetics for the axial next-nearest-neighbor Is ing (ANNNI) model in one and two dimensions by the multispin heat bath dyna mical simulation. This dynamics enables us to overcome the pinning effect a nd to observe the dynamical scaling law for domain growth in the ANNNI mode l at zero temperature. The domain growth exponent is 1/2 isotropically both in the ferromagnetic and the dry (commensurate) antiphase. In the wet (com mensurate) antiphase, however, it is approximately 1/3 in the modulated dir ection, whereas it remains 1/2 in the nonmodulated direction. We suggest th at these exponent values are dictated by 3- and 4-body diffusion-reaction p rocesses of domain walls.