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 Ising (ANNNI) model in one and two dimensions by the multispin 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 nonmodulated direction. We suggest that these exponent values are dictated by 3- and 4-body diffusion-reaction processes of domain walls.