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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 ): 

<img src='content_image/336895.jpg'>

can be compared with the LG Hamiltonian (1). Now we put the constraint of the scale invariance of the partition function: 

<img src='content_image/336896.jpg'>

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: 

<img src='content_image/336897.jpg'>

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: 

<img src='content_image/336898.jpg'>

<img src='content_image/336899.jpg'>

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: 

<img src='content_image/336900.jpg'>

<img src='content_image/336901.jpg'>

