We perform an exact enumeration study of polymers formed from a (quenched)
random sequence of charged monomers ±q0​, restricted to a 2-dimensional
square lattice. Monomers interact via a logarithmic (Coulomb) interaction. We
study the ground state properties of the polymers as a function of their excess
charge Q for all possible charge sequences up to a polymer length N=18. We
find that the ground state of the neutral ensemble is compact and its energy
extensive and self-averaging. The addition of small excess charge causes an
expansion of the ground state with the monomer density depending only on Q.
In an annealed ensemble the ground state is fully stretched for any excess
charge Q>0.Comment: 6 pages, 6 eps figures, RevTex, Submitted to Phys. Rev.