  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 form the weak
segregation limit.
