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## CONCLUSIONS 

In concluding Section we summarize the main results and discuss possible restrictions of the proposed approach. 

The whole set of phenomenological facts about the interrelations between Zeno line, the rectilinear diameter, the binodal and the locus of the critical point revealed in [10– 13] needs in unifying view from the microscopic approach of Statistical Mechanics. The proposed isomorphism allows to search such view in terms of the correspondence between the Hamiltonians of the LG and the fluids with short-ranged pair potentials. In particular it seems natural to connect the thermodynamic potentials for these systems. This allows to determine the parameters of mixing for the fields of the order parameter and the temperature [33]. The results obtained for the locus of the critical point of LJ fluid and critical amplitudes of the equation of state show good correspondence with the results of computer simulations. Though the attractive part of the potential was taken into account in proposed version of the scale invariant mean-field approach the relations Eq. (22),(23) can be generalized to include the repulsive part of the potential. E.g. instead of (23) the following relation arise: 

<img src='content_image/368872.jpg'>

This relation along with the first equation in (10) would give the closed system of equations to determine both n$_{c}$ and z consistently. For the considered case of the LJ potential the repulsive part gives negligible correction so we neglect it here. But in general case the influence of the repulsive part on the locus of the critical point should be taken into account. 

Note that the isomorphism relies on simple geometrical facts among which the tangency of the Zeno-line to the extrapolated liquid-vapor binodal into hypothetic region T → 0 is the most crucial [14]. For real systems the liquid branch is restricted by the triple point and this causes the problem of the correct determination of the parameter n$_{b}$ . Obviously the slope of the Zeno line at n$_{b}$ influence essentially the position of the opposite Zeno state with n → 0. To overcome this difficulty the correct determination of the limiting Zeno state ( T$_{Z}$, 0) was proposed along with the determination of n$_{b}$ form the constraint T$_{Z}$ = a/b where a and b are the corresponding van der Waals constants for the equation of states. In principle it is possible to determine the values of n$_{b}$ using the data for the locus of the triple point and the slope of the binodal using the isomorphism transformation which allows to relate this 

