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Field-theoretic simulations that rely on a partial saddle-point approximation have become powerful tools for studying complex polymer materials. The computational cost of such simulations depends critically upon the efficiency of the iterative algorithm used to identify a partial saddle-point field configuration during each step of a stochastic simulation. We introduce a new algorithm for this purpose that relies on a physically motivated approximation in which the linear response of the density to a small change in a pressure-like field is approximated by the response of a hypothetical homogeneous system. The computational cost of the resulting algorithm is significantly less than that of the commonly used Anderson mixing algorithm. 

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.