The locus of the CP is determined mostly by the attractive part of the interaction potential and the size of the particles (see e.g. [17]). These parameters can be connected with the corresponding ones for the LG model. Suppose that the potential of the d -dimensional system is Φ( r ) = Φ$_{rep}$( r ) + Φ$_{attr}$( r ), where Φ$_{rep}$ , Φ$_{attr}$ are the repulsive and the attractive part correspondingly. Additionally we assume that the attractive part has the power-like behavior Φ$_{rep}$( r ) ∼ r − ( d + ε $^{)}$, ε > 0. Then the corresponding energy of the interaction for the configuration of the number density n ( r ): can be compared with the LG Hamiltonian (1). Now we put the constraint of the scale invariance of the partition function: corresponding to (20) with respect to scaling transformations of n → λ Δ$_{n}$ n and T → λ Δ$_{T}$ T , where λ is the scale parameter. The exponents Δ$_{n}$ and Δ$_{T}$ can be found using standard similarity considerations widely used in condensed matter theory (see e.g. [18]). E.g. for the coordinates of the CP we have: where r$_{c}$ is the mean interparticle distance in the critical state. Therefore from (19) and (22) we can write the relation: which gives the following consistency relation: Thus we obtain the one-parameter group of scaling transformations for the locus of the CP connected with the change of the characteristic scale of the interaction: Eq. (25) is equivalent to the constraint: E$_{int}$ = V 2 ∫ Φ( r$_{12}$ ) n ( r$_{1}$ ) n ( r$_{2}$ ) d r$_{12}$ (20) Z = ∫ e − E int /T d Γ , d Γ = N ∏ i =1 d r$_{i}$ , (21) n$_{c}$ ∼ 1 r d c , T$_{c}$ ∼ Φ$_{attr}$( r$_{c}$ ) = Φ$_{attr}$ ( n − 1 /d c ) , (22) d ln ( T$_{c}$/T$_{Z}$ ) d ln n$_{c}$/n$_{b}$ = d ln Φ$_{attr}$( n − 1 /d c ) d ln n$_{c}$/n$_{b}$ (23) 1 /z = 1 + ε/d . (24) n$_{c}$ ( z ) → n$_{c}$ (0) λ − $^{1}$, T$_{c}$ ( z ) → T$_{c}$ (0) λ ( 1+ ε/d $^{)}$. (25) n$_{c}$ ( λ ) 1+ $^{ε/d}$T$_{c}$ ( λ ) = const . (26) 7