Stability of periodic domain structures in a two-dimensional dipolar model

We investigate the energetic ground states of a model two-phase system with 1/${\mathit{r}}^3$ dipolar interactions in two dimensions. The model exhibits spontaneous formation of two kinds of periodic domain structures. A striped domain structure is stable near half-filling, but as the area fraction is changed, a transition to a hexagonal lattice of almost-circular droplets occurs. The stability of the equilibrium striped domain structure against distortions of the boundary is demonstrated, and the importance of hexagonal distortions of the droplets is quantified. The relevance of the theory for physical surface systems with elastic, electrostatic, or magnetostatic 1/${\mathit{r}}^3$ interactions is discussed.