Methods for Renormalization Group Transformations

As was repeatedly emphasized, away from the phase separation region (i.e. at high temperatures for systems with a UCST), the intersegment interaction in a polymer chain reduces to the existence of segment excluded volume, which manifests itself by swelling (expansion) of polymer coils. These interactions also lead to a correlation of the segment density fluctuations as it occurs in general-type systems near the critical point. 

To study the properties of systems near the critical point, methods of the renormalization group approach have been developed (sec section 2.5) therefore, the development of polymer theory has led to similar methods. 

and Freed have worked out a renormalization method of configurational sptice of polymer chains in several versions. 

Section 5.1 presents renormalization of the Wilson type following Oono and Freed (1981a), and renormalization by Gell-Mann and Low following Oono et al. (1981). In section 5.1, polymer chain renormalization in the momentum space of Kholodcnko and Freed (1983) will be discussed. 

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