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

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 to 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 position of the critical points of the fluids of the Lennard-Jones type can be determined based 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. (C) 2010 American Institute of Physics. [doi:10.1063/1.3457943]