Anisotropic Domain Growth of ANNNI Model at Low Temperatures

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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.