A renormalisation group approach to the entropy of a single polymer

Employing the n to 0 field theoretic analogue the authors derive renormalisation group equations directly for the polymer system which may be solved to exhibit the scaling behaviour of the entropy S(L) of a single polymer of L links. An elegant parametric representation of the crossover from random flight to self-avoiding behaviour as the chain length L or expansion factor alpha =(R 2 )/(R 2 ) theta increases is described, for which explicit representations are constructed to O( epsilon 2 ) in the epsilon expansion. In the asymptotic domain alpha >>1 or L>>1 the expected scaling behaviour is observed.