Accessing the universal phase behavior of block copolymer melts with complex-Langevin field-theoretic simulations

Abstract

The universal phase behavior of block copolymer melts demonstrated previously with particle-based simulations is reproduced using complex-Langevin field-theoretic simulations (CL-FTSs) combined with the Morse calibration. For comparison purposes, the calculations are repeated using conventional Langevin field-theoretic simulations (L-FTSs), where the partial saddle-point approximation (PSPA) is applied to the pressure field. Both FTS methods produce consistent results down to invariant polymerization indices of N̄≈105, implying that the inaccuracies in the PSPA are well compensated for by the Morse calibration. At lower N̄, however, the complex fields of the CL-FTSs become prone to the formation of hot spots, causing the simulations to fail. Previous studies have shown that finite-range interactions can help stabilize CL-FTSs. Aided by the L-FTSs, we locate conditions at N̄=104, under which the universality is expected to hold and the CL-FTSs are stable. While the L-FTSs continue to obey universality, the CL-FTSs deviate significantly. A number of potential explanations are considered, but only one appears credible. Given the documented problems with CL simulations of nonpolymeric models, it is likely that the inconsistency with universality results from a “silent failure” in the CL-FTSs, preceding the formation of hot spots.