A Renormalization Group Approach and the Phenomenological Theory of a Polymer Chain

An intuitive picture of the renormalization transformation of the monomer density field of a polymer chain is given. The picture is justified by the correspondence between complex spin function ϕ 2 and monomer density field, which allows the field-theoretic calculation of the monomer density profile, the radius of gyration, etc. From the renormalization group approach the following conclusions are drawn: 1) a polymer chain can be phenomenologically described with two parameters, 2) the phenomenological two parameters are, however, complicated functions of many (not two) microscopic parameters, 3) the phenomenological parameter z is proportional to N 1/2 (ln N ) 3/22 near the theta point, where N is the length of the polymer, 4) there exists a class of weighted self-interacting walk models which is, at the theta point, globally gaussian but whose intrachain binary interaction does not vanish and is rather attractive.