In this work, we study the global isomorphism between the liquid-vapor equilibrium of the hardcore attractive Yukawa fluid (HCAYF) and that of the Lattice Gas (LG) model of the Ising-like type. The applicability of the global isomorphism transformation and the dependence of its parameters on the screening length of the Yukawa potential are discussed. These parameters determine both the slope of the rectilinear diameter of the liquid-vapor binodal and the Zeno-element, which are the core ingredients of the fluid-LG isomorphism. We compare the Zeno-element parameters with the virial Zeno-line parameters, which are commonly used in the literature for the formulation of generalized law of the correspondent states. It is demonstrated that the Zeno-element parameters appear to be sensitive to the liquid state instability when the interaction potential becomes too short-ranged, while the virial ones do not show any peculiarities connected with this specific of the HCAYF.
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