Decimation along the polymer chain

It is also possible to consider a polymer chain as being made of discrete links embedded in ad-dimensional space, and one can try to perform direct renormalization on polymers. This decimation method consists in representing a polymer of N links as a succession of sequences made of n links, and in considering each 

This renormalization operation thus transforms a chain with N links of length l into a chain with N/n links of length Let R2 be the mean square end-to-end distance of the chain. In the critical domain, we can write 

This computation program, which looks straightforward, was described by de Gennes in 1977,10,11 but it was not easy to put it into practice. However, in 1978, Gabay and Garel12 succeeded in obtaining, with this method, the first term in the expansion of v as a function of e = 4 — d (d = space dimension) namely v = 1/2(1 + s/8 +. ..). However, this result was already known, and at the present time (1988), no algorithm exists which could be used to proceed much further with the decimation method.13 

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