# On internal structure of smaller domains in domain coarsening dynamics of spontaneous Z_2-symmetry breaking in two dimensions

## TL;DR

This paper theoretically analyzes the internal structure of small domains during domain coarsening in 2D systems with Z2 symmetry breaking, confirming that their internal contributions are negligible for key statistical measures.

## Contribution

It provides an analytical validation that the internal structure of small domains can be neglected in statistical analyses of domain coarsening in 2D Z2-symmetry systems.

## Key findings

- Internal structure contribution is negligible for statistical quantities.
- Analytical validation supports previous assumptions in domain coarsening models.
- Results apply to Ising systems and binary superfluids.

## Abstract

The internal structure of domains smaller than the characteristic size in domain coarsening dynamics of $Z_2$ symmetry breaking is evaluated theoretically for different phase ordering systems in two dimensions. In the previous works on (non-) conserved Ising systems and binary superfluids, the statistical properties of smaller domains are analyzed by assuming that the contribution from its internal structure is negligible. It is shown that this assumption is justified analytically with respect to the statistical quantities, such as domain area, domain-wall length and superfluid circulation, according to the empirical dynamic scaling law for the smaller domains.