How to turn real substance liquid–gas coexistence curve in binodal of lattice gas

A linear fractional transformation is proposed, which establishes the relationship between the liquid–gas coexistence curve of real substances and binodal of lattice models. Herewith the substance critical point with some density ρc and some temperature Tc is mapped in the critical point of a lattice model with density x = 0.5 and temperature t = 1. We found the ‘lattice analogues’ for binodals of mercury, cesium argon, ammonia and binodals of two model systems (van der Waals and Lennard-Jones). They are compared with analytical and numerical binodals known in the theory of lattice systems.