First order phase transitions and the thermodynamic limit

TL;DR

This paper investigates how phase coexistence and Maxwell construction emerge in mean field models of phase transitions as systems approach the thermodynamic limit, highlighting the role of localized structures.

Contribution

It demonstrates the emergence of Maxwell construction in mean field models for phase transitions from finite systems to the thermodynamic limit, emphasizing the importance of localized states.

Findings

Maxwell line states depend on mean density

Localized structures are crucial in the thermodynamic limit

Models include Cahn-Hilliard and phase field crystal

Abstract

We consider simple mean field continuum models for first order liquid-liquid demixing and solid-liquid phase transitions and show how the Maxwell construction at phase coexistence emerges on going from finite-size closed systems to the thermodynamic limit. The theories considered are the Cahn-Hilliard model of phase separation, which is also a model for the liquid-gas transition, and the phase field crystal model of the solid-liquid transition. Our results show that states comprising the Maxwell line depend strongly on the mean density with spatially localized structures playing a key role in the approach to the thermodynamic limit.