Phase transitions with semi-diffuse interfaces

In this paper, we examine new “phase-field” models with semi-diffuse interfaces. These models have the property that the −1/+1 planar phase transitions take place over a finite interval. The models also support multiple interface solutions with interfaces centered at arbitrary points L₁<L₂L_N. These solutions correspond to local minima of an entropy functional (see (3.3) and (3.7)) rather than saddle points and are dynamically stable. The classical models have no such exact solutions but they do support solutions with N equally spaced transition points where the order parameter transitions between values p_min(N) and p_max(N) satisfying −1<p_min(N)<0<p_max(N)<1. These solutions of the classical model are saddle points of the entropy functional associated with those models and are not dynamically stable.