Ground states of two-dimensional polyampholytes

We perform an exact enumeration study of polymers formed from a (quenched) random sequence of charged monomers [Formula Presented], restricted to a two-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 [Formula Presented] for all possible charge sequences up to a polymer length [Formula Presented]. We find that the ground state of the neutral ensemble is compact and its energy extensive and self-averaging. The addition of a small excess charge causes an expansion of the ground state with the monomer density depending only on [Formula Presented]. In an annealed ensemble the ground state is fully stretched for any excess charge [Formula Presented].