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

TL;DR

This paper develops a thermodynamically consistent phase-field theory incorporating pair correlations, revealing their significant effects on interface structure and phase separation, especially under strong interactions, which are overlooked by mean-field approaches.

Contribution

It introduces a new Cahn-Hilliard free energy model that includes pair correlations derived from the Bethe-Guggenheim approximation, advancing understanding of interface broadening and phase separation.

Findings

Pair correlations cause interface broadening at high interaction strengths.

Entropy-driven interface delocalization is observed, not captured by mean-field theory.

Thermodynamic consistency requires including pair correlations for accurate modeling.

Abstract

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.