Global isomorphism between the Lenard-Jones fluids and the Ising model

TL;DR

This paper proposes a global isomorphism between Lennard-Jones fluids and the Ising model, explaining linear laws and phase diagram features through a unified lattice-gas framework.

Contribution

It introduces a novel global isomorphism approach linking Lennard-Jones fluids with the Ising model, clarifying phase diagram linearities and critical point relations.

Findings

Linear rectilinear diameter law explained by isomorphism

Position of critical points derived from scaling symmetry

Phase diagram of fluids isomorphic to lattice gas diagram

Abstract

The interpretation of the linear character of the observable classic rectilinear diameter law and the linear character of the Zeno-line (unit compressibility line Z=1) on the basis of global isomorphism between Ising model (Lattice Gas) and simple fluid is proposed. The correct definition of the limiting nontrivial Zeno state is given and its relation with the locus of the critical point is derived within this approach. We show that the liquid-vapor part of the phase diagram of the molecular fluids can be described as the isomorphic image of the phase diagram of the Lattice Gas. It is shown how the the position of the critical points of the fluids of the Lenard-Jones type can be determined basing on the scaling symmetry. As a sequence the explanation of the well known fact about "global" cubic character of the coexistence curve of the molecular fluids is proposed.