Polymer correlation functions and spurious singularities in n=0 field theory.

Abstract

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.