Ordering dynamics of one-dimensional Bloch wall system and domain size distribution function

The dynamics of domain size distribution in the ordering process for a one-dimensional classical anisotropic $\mathrm{XY}$ model is studied with a reduced equation of motion for the assembly of domain sizes. The system possesses two types of the domain wall structures, the Néel or Bloch walls, depending on the strength of magnetization anisotropy. In the Néel wall situation the neighboring walls interact with one another in only an attractive way. On the other hand, in the Bloch one, these walls interact in either an attractive or a repulsive way depending on their chiralities. For the Bloch wall situation, we found that the domain size distribution is characterized by solitonlike translational motion with a function form $h\left(y-y\right(t\left)\mathrm{}\right)$ and a characteristic domain size $y\left(t\right)\mathrm{}$ for the domain size y. This is in contrast to that in the Néel wall situation, which can be described as a scaling-type distribution function $g[y/l(t\left)\mathrm{}\right]/l\left(t\right),$ as was obtained by Nagai and Kawasaki, with a certain scaling length $l\left(t\right).$ We discuss why such a solitonlike motion appears instead of the scaling-type distribution function, show a proof for the absence of the scaling-type distribution, a qualitative estimation for the distribution function in the Bloch wall situation, and an analysis for the realization probability of a specified twistness.