Loop expansion in polymer field theory: application to phase separation

Liquid-liquid phase separation underlies phenomena ranging from protein condensate formation to the phase coexistence of synthetic polymers. In this talk, we develop a field theoretic loop expansion in homopolymer systems by identifying the inverse polymer density ρ^{-1} as the Planck constant ℏ in quantum field theory. The 1-loop approximation is known as the random phase approximation (RPA) and has been extensively applied to many (hetero)polymer systems. We calculate the leading-order (2-loop) and next-to-leading-order (3-loop) corrections to the RPA free energy, denoted as RPA+ and RPA++, respectively. Testing the binodal predicted by the RPA+ against molecular dynamics simulations of bead-spring chains with Gaussian pair interactions, we find that the RPA+ qualitatively improves the dilute-phase coexistence density over the RPA, while the critical point error remains comparable to that of the RPA. Our results establish the loop expansion as a systematic route for refining the RPA-based binodal predictions for polymer phase separation.
This talk is based on arXiv: 2605.01261.