Polymer correlation functions and spurious singularities inn=0field theory

We use previous results for Goldstone modes of the n-component ($S^2$ ${)}^2$ field theory to analyze polymer solutions described formally by setting n=0 in the field-theoretic results. For n<1 certain vertex functions show spurious poles which, however, can be shown to cancel exactly in all observable quantities. The poles are related to the ‘‘negative susceptibility’’ problem and can be traced back to the fact that one-line irreducibility ruins the screening of the Goldstone singularities. One-line irreducible vertex functions therefore are not adapted to a treatment of the magnetization curve. Reducing the theory further to one-vertex irreducible parts, we give a formulation of polymer correlation functions manifestly analytic over the entire magnetic phase diagram. We present one-loop calculations of the end-point correlations and the density correlations in a polymer solution which confirm the general analysis. The results are in full agreement with qualitative ideas on screening and the structure of semidilute solutions. Recent claims on the existence of a new phase of collapsed polymer chains are thus refuted.