Langevin Field-Theoretic Simulation for ABC-type Polymer Systems*

In this research, we investigate how the partial saddle point approximation method can overcome the sign problem in polymer field theory simulations of the block copolymers (BCPs). While this approach has shown success in studying fluctuation effects in AB-type polymer systems such as diblock copolymer melts, star-shaped copolymer melts, and BCP-homopolymer blends, its applicability to ABC-type polymer systems has remained uncertain. In three-component systems, the presence of two exchange fields with real or imaginary values depending on the three Flory-Huggins interaction parameters, poses unique challenges. After eliminating imaginary fields by applying the saddle point approximation, the remaining number of fluctuating fields may be less than two, and it may be insufficient to appropriately account for the fluctuation effect. In this work, we employ Langevin field-theoretic simulation (L-FTS), a popular method of the partial saddle point approximation, to investigate how order-to-disorder transition points vary with the number of fluctuating fields. Our findings reveal that at least one field fluctuates unless all three Flory-Huggins interaction parameters are negative, and even a single fluctuating field can effectively represent the majority of the fluctuation effect. Moreover, we develop our deep learning-accelerated L-FTS software for multi-component systems available as open source, facilitating further research in this area.