Conformation Space Renormalization of Polymers. 4. Equilibrium Properties of the Simple Ring Polymer Using Gell-Mann-Low Type Renormalization Group Theory

The method of Oono, Ohta, and Freed is used to derive static properties of a ring polymer above θ the point. This method uses the technique of dimensional regularization as formulated in conformational space where monomers are specified by their positions in space and along the chain. The distribution function for an internal vector of a ring polymer is determined by using the renormalization group analysis with an expansion in d = 4-ε space, d being the spatial dimensionality. The distribution function yields exponents describing the asymptotic, long- and short-range, behavior of polymer rings. These exponents are the same to order e as those for linear chains.