Polymer Field Theory for Multimonomer Incompressible Models: Symmetric Formulation and ABC Systems

We present a symmetric formulation of polymer field theory for incompressible systems containing any number M of monomer types, in which all monomers are treated on an equal footing. This is proposed as an alternative to the multispecies exchange formulation, which imposes incompressibility by eliminating one monomer type. The symmetric formulation is shown to correspond to the incompressible limit of a corresponding compressible model, and to reduce in the case M = 2 to the usual formulation of field theory for incompressible AB systems. An analysis of ABC systems (M = 3) identifies ranges of interaction parameter values in which a fully fluctuating field theory requires one, two or three imaginary-valued fields. ABC systems with parameters that satisfy the Hildebrand solubility parameter approximation are shown to require only one imaginary pressure-like field, much like AB systems. Generalization of the partial saddle-point approximation to M > 2 is discussed.