Domain growth and topological defects in an Ising model with competing interactions.

Abstract

We have studied the kinetics of domain growth in the (4\ifmmode\times\else\texttimes\fi{}1) uniaxial [or (2,2)] phase of the two-dimensional anisotropic next-nearest-neighbor Ising (ANNNI) model with Monte Carlo methods using Glauber dynamics. The growth is shown to be spatially anisotropic, with the anisotropy depending strongly on the anisotropy parameter \ensuremath{\alpha}. In addition to this, a more abrupt change is found as one crosses a wetting transition line in the model. Despite this a dynamical exponent n\ensuremath{\simeq}0.5 is obtained at low temperatures for all values of \ensuremath{\alpha}. To explain these results, a phenomenological theory of domain growth developed originally for the clock model is extended to include the uniaxial (4\ifmmode\times\else\texttimes\fi{}1) phase. In particular, it is demonstrated that the more abrupt change near the wetting transition occurs due to the disappearance of a vertex-antivertex configuration present in the dry region. Also, the ANNNI model with conserved dynamics is shown to belong to a different universality class than a model with a symmetric p=4 phase studied recently.