On the determination of phase boundaries via thermodynamic integration across coexistence regions

TL;DR

This paper explores using thermodynamic integration with pressure equations of state in canonical simulations to accurately locate phase boundaries, especially in metastable regions, demonstrated on the Lennard-Jones model.

Contribution

It introduces a system-size reduction approach to mitigate metastability issues and compares TI's effectiveness in different phase transition regions.

Findings

TI accurately predicts liquid-vapor coexistence.

TI fails in solid-liquid transition, requiring alternative methods.

Smaller systems reduce metastability problems.

Abstract

Specialized Monte Carlo methods are nowadays routinely employed, in combination with thermodynamic integration (TI), to locate phase boundaries of classical many-particle systems. This is especially useful for the fluid-solid transition, where a critical point does not exist and both phases may notoriously go deeply metastable. Using the Lennard-Jones model for demonstration, we hereby investigate on the alternate possibility of tracing reasonably accurate transition lines directly by integrating the pressure equation of state computed in a canonical-ensemble simulation with local moves. The recourse to this method would become a necessity when the stable crystal structure is not known. We show that, rather counterintuitively, metastability problems can be alleviated by reducing (rather than increasing) the size of the system. In particular, the location of liquid-vapor coexistence can exactly be predicted by just TI. On the contrary, TI badly fails in the solid-liquid region, where a better assessment (to within 10\% accuracy) of the coexistence pressure can be made by following the expansion, until melting, of the defective solid which has previously emerged from the decay of the metastable liquid.