Parametric representation of the dilute polymer system to O(ϵ2): crossover from Wilson-Fisher to gaussian fixed point as the Flory temperature is approached

It is well known that the properties of scaling and universality exhibited by the polymer system have a very natural description in terms of the critical behaviour of an analogous magnetic system. This analogy is used to derive renormalisation-group equations directly for the polymer system. Solving these renormalisation-group equations a compact parametric description is obtained of the crossover from the Wilson-Fisher to gaussian fixed point displayed by the mean square size of a polymer (R 2 ) and the second A 2 and third A 3 virial coefficients correct to O( epsilon 2 ) in d=4- epsilon spatial dimensions.