The application of the global isomorphism to the study of liquid-vapor equilibrium in two and three dimensional Lenard-Jones fluids

TL;DR

This paper explores the relationship between the liquid-vapor coexistence curves of Lennard-Jones fluids and the Ising model in two and three dimensions using the global isomorphism approach, comparing theoretical predictions with simulation data.

Contribution

It applies the global isomorphism method to connect Lennard-Jones fluid phase behavior with the Ising model, utilizing exact and numerical results for improved understanding.

Findings

Exact Onsager solution used for 2D Lennard-Jones binodal

Comparison with simulation data validates the approach

Discussion on the singularity of the binodal diameter

Abstract

We analyze the interrelation between the coexistence curve of the Lennard-Jones fluid and the Ising model in two and three dimensions within the global isomorphism approach proposed earlier [V. L. Kulinskii, J. Phys. Chem. B \textbf{114} 2852 (2010)]. In case of two dimensions we use the exact Onsager result to construct the binodal of the corresponding Lennard-Jones fluid and compare it with the results of the simulations. In the three dimensional case we use available numerical results for the Ising model for the corresponding mapping. The possibility to observe the singularity of the binodal diameter is discussed.