Coarsening dynamics of field-induced inversion domain walls in smectic-C films

We present a numerical study on the phase-ordering kinetics of the smectic-C film under an external magnetic field. Due to the inversion symmetry of the director fields, the external held induces Ising-like inversion domain walls in this system. It is observed that the usual dynamic scaling based on a single dominant length scale is violated for the Ising-like order parameter, except in the asymptotic lime Limit. This scaling violation is attributed to the existence of point defects along the domain walls and the corresponding length scale (the average separation between point defects) in addition to the average domain size. The correlation functions exhibit a very slow approach to the asymptotic scaling limit, with early-time correlation functions characterized by large curvature near the origin, gradually crossing over to Ising-like correlation functions at the late-time stage. In spite of this apparent violation of dynamic scaling, we find that the above slow approach toward the asymptotic pure Ising scaling function follows a universal functional form when the time is properly rescaled in terms of the field-dependent time scale.