  Using the complex Langevin sampling strategy, field theoretic simulations are
performed to study the equilibrium phase behavior and structure of symmetric
polycation-polyanion mixtures without salt in good solvents. Static structure
factors for the segment density and charge density are calculated and used to
study the role of fluctuations in the electrostatic and chemical potential
fields beyond the random phase approximation. We specifically focus on the role
of charge density and molecular weight on the structure and complexation
behavior of polycation-polyanion solutions. A demixing phase transition to form
a ``complex coacervate'' is observed in strongly charged systems, and the
corresponding spinodal and binodal boundaries of the phase diagram are
investigated.
