FIG. 2: Critical density n$_{c}$ for the potential (18) of the d -dimensional according to Eq. (29) (dashed line is the guide for an eye) and the packing fraction η ( T, d ) given by Eq. (33) (grey lines) . FIG. 3: Binodal for 2D Lenard-Jones fluid with Φ$_{attr}$( r ) ∼ r − 6 calculated as the isomorphic image of the binodal for 2 D Lattice Gas (Ising model) in accordance with (8). the binodal for 2D LJ fluid can be easily obtained (see Fig. 3) and compared with the results of the computer simulations [28]. Also the inference that the cubic character of the binodal for real systems is the consequence of the cubic character of the binodal for the Ising model. So one can expect that the coexistence curve of the 3D Ising model is described in the “zeroth approximation“ by the algebraic cubic curve in analogy with (34): where f ( t ) is analytic function of the temperature. In particular the isomorphism transformation (8) applied to (35) allows to connect the x = 1 / 2 ± f ( t ) 1 / 3 ⇒ t ( x ) = f − $^{1}$( | 2 x − 1 | $^{3}$) , f (1) = 0 (35) 11