Direct calculation of the solid-liquid Gibbs free energy difference in a single equilibrium simulation

TL;DR

This paper presents an efficient method for directly calculating the solid-liquid Gibbs free energy difference in a single equilibrium simulation, improving phase diagram computations for model systems like Lennard-Jones.

Contribution

The paper introduces the interface pinning (IP) method combined with Newton-Raphson for precise, single-simulation Gibbs free energy difference calculations, with detailed error analysis.

Findings

High-precision coexistence line computation demonstrated

Effective combination of IP and Newton-Raphson methods

Analysis of statistical and systematic errors

Abstract

Computing phase diagrams of model systems is an essential part of computational condensed matter physics. In this paper we discuss in detail the interface pinning (IP) method for calculation of the Gibbs free energy difference between a solid and a liquid. This is done in a single equilibrium simulation by applying a harmonic field that biases the system towards two-phase configurations. The Gibbs free energy difference between the phases is determined from the average force that the applied field exerts on the system. As a test system we study the Lennard-Jones model. It is shown that the coexistence line can be computed efficiently to a high precision when the IP method is combined with the Newton-Raphson method for finding roots. Statistical and systematic errors are investigated. Advantages and drawbacks of the IP method are discussed. The high pressure part of the temperature-density coexistence region is outlined by isomorphs.