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

Department for Theoretical Physics, Odessa National University, Dvoryanskaya 2, 65026 Odessa, Ukraine 

V.L. Kulinskii ∗ 

## 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. 

PACS numbers: 05.70.Jk, 64.60.Fr, 64.70.F 

