Optimal periodic structures with general space group symmetries in the Ohta–Kawasaki problem

We consider the problem of rigorously computing periodic minimizers to the Ohta–Kawasaki energy. We develop a method to prove existence of solutions and determine rigorous bounds on the distance between our numerical approximations and the true infinite dimensional solution and also on the energy. We use a method with prescribed symmetries to explore the phase space, computing candidate minimizers both with and without experimentally observed symmetries. We find qualitative differences between the phase diagram of the Ohta–Kawasaki energy and self consistent field theory when well away from the weak segregation limit.