LJ “6-12“ fluid 2D 3D 4D 5D T$_{Z}$ 2 4 8 20 n$_{b}$ σ d 0.91 0.965 1.342 2.54 T$_{B}$ 1.56 3.418 9.01 40.4 TABLE I: The results of computation of T$_{Z}$ and T$_{B}$ for LJ potential (18) for different dimensions and the packing factor n$_{b}$ σ $^{d}$. The locus of the CP is obtained easily according to (29) and (31) (see Fig. 1,2). The comparison with the results of the simulations is in Table II. Note that expressions (29) and (31) allow to clarify the fact noted in [20] about different characters of the dependencies of T$_{c}$ and n$_{c}$ on the dimensionality d . The value T$_{c}$ strongly depends on the dimension because of the dependence of T$_{B}$ while the d -dependence of n$_{c}$ is rather weak. Note that nonmonotonic dependence of the critical density on the number of dimensions d can be interpreted in terms of the proposed isomorphism as follows. The equilibrium interparticle distance for the LJ potential (18) is r$_{0}$ = σ 2 1 / 6 and can be considered as the spacing of the cubic lattice for the LG. The effective radius r$_{eff}$ of excluded volume occupied by the particle from the physical point of view can be defined by the obvious energetic condition: So the packing of spheres of radii r$_{eff}$ on the corresponding cubic lattice can be found as The existence of global isomorphism also provides the explanation of the fact about the cubic form of the binodal for real molecular fluids. The fact that the shape of the binodal is almost cubic and characterized by the effective exponent β$_{eff}$ = ∂ ln ϕ ∂ ln τ ≈ 1 / 3 , ϕ = n$_{l}$ − n$_{g}$ n$_{c}$ in a wide temperature interval for the system with short range interactions was discovered long ago by J. E. Verschaffelt [21–23] (see also [6]) and since then has been confirmed by where V ( d ) = 2 π d/ 2 Γ( d $_{2}$) is the volume of the unit ball in d dimensions. Obviously n$_{c}$ depends on η ( T, d ) monotonically. The dependence of η ( T, d ) on the dimension d is shown on Fig. 2 by grey lines and shows the minimum in the interval d ≤ 4 in dependence on the temperature. Note that at T = 0, when r$_{eff}$ = σ this minimum reaches exactly at d = 4. Φ(2 r$_{eff}$ ) = T ⇒ r$_{eff}$ ( T ) . (32) η ( T, d ) = 2 d/ 6 σ d V ( d ) r$_{eff}$ ( T ) d , (33) 9