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

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.

15 pages, 3 figures (2 figures added and the references)

References in corpus (4)

• Critical point and coexistence curve properties of the Lennard-Jones fluid: A finite-size scaling study
• The Magnetization of the 3D Ising Model
• Simple geometrical interpretation of the linear character for the Zeno-line and the rectilinear diameter
• Simulation of phase transitions in highly asymmetric fluid mixtures

Cited by in corpus (11)

• The critical compressibility factor value: associative fluids and liquid alkali metals
• Generalized principle of corresponding states and the scale invariant mean-field approach
• The unified picture for the classical laws of Batschinski and the rectilinear diameter for molecular fluids
• The critical compressibility factor of fluids from the Global Isomorphism approach
• The Vliegenthart-Lekkerkerker relation. The case of the $Mie$-fluids
• The application of the global isomorphism to the study of liquid-vapor equilibrium in two and three dimensional Lenard-Jones fluids
• Surface tension of molecular liquids: Lattice gas approach
• Hard-core attractive Yukawa fluid global isomorphism with the lattice gas model
• The application of the global isomorphism to the surface tension of the liquid-vapor interface of the Lennard-Jones fluids
• Liquid-gas state regularities as a manifestation of global isomorphism with the Ising model
• Supercritical Crossover Lines in the Cell Fluid Model