Numerics and analysis of Cahn–Hilliard critical points

We explore recent progress and open questions concerning local minima and saddle points of the Cahn–Hilliard energy in [Formula: see text] and the critical parameter regime of large system size and mean value close to [Formula: see text]. We employ the String Method of E, Ren, and Vanden-Eijnden—a numerical algorithm for computing transition pathways in complex systems—in [Formula: see text] to gain additional insight into the properties of the minima and saddle point. Motivated by the numerical