Preserving Positivity: Developments in Density-Explicit Field-Theoretic Simulations

Field-theoretic simulations (FTS) are numerical treatments of polymer field theory models that go beyond the mean-field level and account for composition fluctuations. Such simulations have successfully captured a range of mesoscopic phenomena. Modern field-based simulations of polymeric fluids rely upon the auxiliary field theory framework that uses Hubbard-Stratonovich transformations to invoke the particle-to-field transformation; the transform introduces an inverse potential limiting the functional form of the non-bonded potentials. Lifting the restriction on non-bonded potentials will facilitate studies of a broad range of systems whose description requires higher-body or more complex potentials. A candidate field theory is the hybrid density-explicit auxiliary field (DE-AF) theory, which retains each species' density field in addition to a conjugate auxiliary field. Although the DE-AF theory is not new, FTS simulations in the DE-AF framework have yet to be realized up to this point. A significant challenge is maintaining the nonnegative character of the density field during stochastic evolution. For this purpose, we utilize positivity-preserving schemes that allow for the first stable and efficient FTS simulations of the DE-AF theory.