Thermodynamically Consistent Phase-Field Theory Including Nearest-Neighbor Pair Correlations Explains Failure of Mean-Field Reasoning

Most of our current understanding of phase separation is based on ideas that disregard correlaions. Here we illuminate unexpected effects of correlations on the structure and thermodynamics of interfaces and in turn phase separation, which are decisive in systems with strong interactions. Evaluating the continuum limit of the Ising model on the Bethe-Guggenheim level, we derive a Cahn-Hilliard free energy that takes into account pair correlations. For a one-dimensional interface in a strip geometry these are shown to give rise to an effective interface broadening at interaction strengths near and above the thermal energy, which is verified in the Ising model. Interface broadening is the result of an entropy-driven interface delocalization, which is not accounted for in the widely adopted mean field theory. Pair correlations are required for thermodynamic consistency as they enforce a thermodynamically optimal local configuration of defects and profoundly affect nucleation and spinodal decomposition at strong coupling.