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Using a diblock copolymer melt as a model system, we show that complex Langevin (CL) simulations constitute a practical method for sampling the complex weights in field theory models of polymeric fluids. Prior work has primarily focused on numerical methods for obtaining mean-field solutions—the deterministic limit of the theory. This study is the first to go beyond Euler- Maruyama integration of the full stochastic CL equations. Specifically, we use analytic expressions for the linearized forces to develop improved time integration schemes for solving the nonlinear, nonlocal stochastic CL equations. These methods can decrease the computation time required by orders of magnitude. Further, we show that the spatial and temporal multiscale nature of the system can be addressed by the use of Fourier acceleration.

Numerical Solutions of the Complex Langevin Equations in Polymer Field Theory