Stabilizing complex-Langevin field-theoretic simulations for block copolymer melts

Abstract

Complex-Langevin field-theoretic simulations (CL-FTSs) provide an approximation-free method of calculating fluctuation corrections to the self-consistent field theory (SCFT) of block copolymer melts. However, the complex fields are prone to the formation of hot spots, which cause the method to fail. This problem has been attributed to an invariance under complex translations, which allows the system to drift away from the real-valued saddle-point of SCFT. Here, we apply dynamical stabilization to CL-FTSs of diblock copolymer melts, whereby the drift is suppressed by a small imaginary force on the composition field. The force needs to be sufficient to hold the system near the real saddle-point, but also small enough not to significantly bias the statistics. Although larger forces are required as the fluctuations become more intense, we are able to lower the invariant polymerization indices of the CL-FTSs by several orders of magnitude, before this becomes a problem. The new CL-FTS results are then used to test conventional Langevin simulations (L-FTSs), in which the instability is removed by a partial saddle-point approximation (PSPA) to the pressure field. As found previously, the L-FTSs agree accurately with the CL-FTSs, provided that the comparison is performed using a Morse calibration.