  We examine the statistics of conformations of a linear polymer in a solvent.
The polymer is allowed to form double polymers. We closely follow a classical
technique to derive a field theory for the problem from an $O\left(n\right)$
symmetric spin model. The field theory is a model for RNA or DNA with constant
binding energy per monomer.
  It is shown that there is a stable renormalization group fixed point, at
which the double polymer decouples from the single-strand polymer and becomes a
branched polymer of the conventional type with a three-point interaction. To
reach this fixed point, at least one parameter must be adjusted. The critical
dimension is eight. Fisher-renormalization, equation of state and critical
exponents are reproduced in this limit. The single-strand polymer depends on
the double-strand polymer and disappears at the critical point, but has its own
critical exponents.
