INTRODUCTION Since the seminal doctoral thesis of van der Waals [1] where the Principle of the Cor- responding States was formulated the search for the unifying principles for the description of the variety of thermodynamical properties of complex matter is the key point of statis- tical physics. By the rigorous methods of the Statistical Mechanics the universal character of the van der Waals (vdW) equation was demonstrated and the numerous extension were proposed [2]. The consequences derived from the vdW equation and the observed devia- tions became the driving force for the further theoretical developments. One of the main achievement of van der Waals was the description of the phase liquid-gas equilibrium which terminated at the corresponding critical point (CP). It opened the possibility to connect the observable thermodynamic quantities with the characteristics of intermolecular interactions. In the modern theory of the Critical Phenomena the ideology of the isomorphism classes of the critical behavior provides the description of the real systems using the results obtained for the model systems like lattice models [3]. In particular the molecular liquids with short range interactions of the Lenard-Jones (LJ) type belong to the isomorphism class of the Ising model. The latter can be easily mapped to the Lattice Gas (LG) model, which is determined by the Hamiltonian: where n$_{i}$ = 0 , 1 whether the site is empty or occupied correspondingly. The quantity J is the energy of the site-site interaction of the nearest sites i and j , µ is the chemical potential. The temperature variable corresponding to the Hamiltonian (1) is denoted as t . The order parameter is the probability of occupation of the lattice site x = 〈 n$_{i}$ 〉 and serves as the analog of the density. The phase diagram of the LG is symmetrical with respect to the line x$_{0}$ = 1 / 2 and formally extends up to the low temperature region t → 0, where the limiting states x = 0 and x = 1 exist only. Two of the consequences of the vdW equation are of primary importance for our consid- eration. The first one is the well-known rectilinear law for the diameter of the coexistence curve in terms of the particle density n and the thermodynamic temperature T : H = − J ∑ 〈 ij 〉 n$_{i}$ n$_{j}$ − µ ∑ i n$_{i}$ , (1) n$_{d}$ = n$_{liq}$ + n$_{gas}$ 2 n$_{c}$ = 1 + A | τ | + . . . , τ = T − T$_{c}$ T$_{c}$ (2) 2