Principles of direct renormalization

The most important quantities, from a theoretical point of view, are  

In particular, this function leads to the mean square end-to-end distance of an 

On the other hand, the second virial coefficient is given by (S, S) and F(S) since according to (10.5.6) we have 

The area S characterizes the size of non-interacting Brownian chains corresponding to z = 0. When z becomes large, the size of the chains becomes also very large and in order to represent the physical situation in the domain z 1, it is necessary to use another scale  

For an isolated self-interacting polymer, we can define an area S as follows 

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