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We analyze the interrelation between the coexistence curve of theLennard-Jones fluid and the Ising model in two and three dimensions within theglobal isomorphism approach proposed earlier [V. L. Kulinskii, J. Phys. Chem. B\textbf{114} 2852 (2010)]. In case of two dimensions we use the exact Onsagerresult to construct the binodal of the corresponding Lennard-Jones fluid andcompare it with the results of the simulations. In the three dimensional casewe use available numerical results for the Ising model for the correspondingmapping. The possibility to observe the singularity of the binodal diameter isdiscussed.

The application of the global isomorphism to the study of liquid-vapor equilibrium in two and three dimensional Lenard-Jones fluids