Size relation for surface systems with long-range interactions

From the minimization of the free energy it follows that strained layers and, more generally, surface systems governed by effective long-range interactions decaying as 1/r² will exhibit periodically ordered domain structures. We show that there exists a firm relation between the size of a single domain (at low domain concentrations) and the minimum separation between them at intermediate concentrations. This size ratio is about 1:3. It is independent of the symmetry (striped or various two-dimensional arrangements) of the domain pattern. This size relation is indeed observed for a variety of different systems.