Defect Structures in the Growth Kinetics of the Swift-Hohenberg Model

Abstract

The growth of striped order resulting from a quench of the two-dimensional Swift-Hohenberg model is studied in the regime of a small control parameter and quenches to zero temperature. We introduce an algorithm for finding and identifying the disordering defects (dislocations, disclinations and grain boundaries) at a given time. We can track their trajectories separately. We find that the coarsening of the defects and lowering of the effective free energy in the system are governed by a growth law $L(t)\approx t^{x}$ with an exponent x near 1/3. We obtain scaling for the correlations of the nematic order parameter with the same growth law. The scaling for the order parameter structure factor is governed, as found by others, by a growth law with an exponent smaller than x and near to 1/4. By comparing two systems with different sizes, we clarify the finite size effect. We find that the system has a very low density of disclinations compared to that for dislocations and fraction of points in grain boundaries. We also measure the speed distributions of the defects at different times and find that they all have power-law tails and the average speed decreases as a power law.