Exact critical exponents for a polymer melt

It is well-known that in a polymer melt as in a semi-dilute solution, the size exponent has the trivial value v = 1/2. However, for a melt, it is also possible to define exponents aM as was done for dilute solutions (see Section 3.3) as before, these exponents are directly related to the partition functions associated with a network [see eqns (12.3.64) and (12.3.65)]. The values of aM in the present case are not obvious. However, the exact values in two-dimensions 

Toulouse, G. and Pfeuty, P. (1975). Introduction au groupe de renormalisation et a ses applications. Presse Universitaines de Grenoble. Ma Shang-Keng, (1976). Modern theory of critical phenomena. Benjamin, New York. 

Brezin, E., Le Guillou, J.C., and Zinn-Justin, J. (1976). Field theoretical approach to critical phenomena. In Phase transitions and critical phenomena (eds. C. Domb and M.S. Green), Vol. 6. p, 125. Academic Press. 

(1978). Field theory, the renormalization group and critical phenomena. McGraw-Hill. Also 2nd edn (1984), Worlcl Scientific, Singapore. 

de Gennes, P.G. (1979). Scaling concepts in polymer physics, p. 290. Cornell University Press, Ithaca, NY. 

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