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

We analyze the interrelation between the coexistence curve of the Lennard-Jones fluid and the Ising model in two and three dimensions within the global isomorphism approach proposed earlier [V. L. Kulinskii, J. Phys. Chem. B 114, 2852 (2010)]. In case of two dimensions, we use the exact Onsager result to construct the binodal of the corresponding Lennard-Jones fluid and compare it with the results of the simulations. In the three-dimensional case, we use available numerical results for the Ising model for the corresponding mapping. The possibility to observe the singularity of the binodal diameter is discussed.