2D Phase Diagram for Minimizers of a Cahn–Hilliard Functional with Long-Range Interactions

This paper presents a two-dimensional investigation of the phase diagram for global minimizers to a Cahn–Hilliard functional with long-range interactions. Based upon the H⁻¹ gradient flow, we introduce a hybrid numerical method to navigate through the complex energy landscape and access an accurate depiction of the ground state of the functional. We use this method to numerically compute the phase diagram in a (finite) neighborhood of the order-disorder transition. We demonstrate a remarkably strong agreement with the standard asymptotic estimates for stability regions based upon a small parameter measuring perturbation from the order-disorder transition curve.