Renormalization group scale transformation

Figure 2.68 Grid model of a porous medium (left) and renormalization group transformation replacing a cluster of grid cells by a unit cell of larger scale (right).

The renormalization group transformation of the Wilson type for the macromolecular conformational space Ks is composed of the scaling transformation Ss and KsMlanoff s transformation /Cs -... 

The chief feature is that the experimentally measured quantities become actually insensitive to the fine elements of the structure instead, they perceive just the scaled-enlarged pattern of the system s structure. Such a bridge between the theuretico-iiiatlieiiiatieal procedure of scaling the Hamiltonian (the renormalization group transformation) and an experimentally measured quantity offers considerable scope for studies on substances in their critical state. 

However, only in renormalization group methods did the ideas of step-by-step scaling transformations find their rigorous analytical and beautiful realization. One of such procedures was put forward by de (Jennes and described in his book. 

An alternative derivation of Eq. (B-9) is based on the decimation procedure. Rigour-ously, a detailed analysis in terms of renormalization group trajectories (cf. Ref. 22, Chap. 11 and Ref. 37) is required. This type of procedure is the theoretical basis behind the so-called blob model. The excluded volume effects are important at short-range scale, within a blob containing g monomers. At larger scale excluded volume interactions are screened. The mean-field approach will, therefore, be valid if the blob of size and volume is taken as the site. Then, in order to describe the thermodynamics, the following transformations must be carried out in Eq. (B-6)... 

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