Generalized principle of corresponding states and the scale invariant mean-field approach

In this paper we apply the global isomorphism approach [V.~L. Kulinskii, J. Phys. Chem. B \textbf{114} 2852 (2010)] between the Lennard-Jones fluids and Lattice Gas model to the study of the liquid-vapor equilibrium for the systems with the short-ranged potentials like Buckingham and the $Mie$-potentials. The estimates for the critical point locus correlate quite well with the available numerical data. Also within the proposed approach we give the explanation for the correlation between the value of the second virial coefficient at the critical temperature and the particle volume found in [G. A. Vliegenthart and H. N. W. Lekkerkerker, J. Chem. Phys. \textbf{112} 5364 (2000)].