Statistical segment length in complex-Langevin field-theoretic simulations

Abstract

A method is introduced for calculating the average end-to-end length, R_0, of polymers in complex-Langevin field-theoretic simulations (CL-FTSs). The statistical segment length, a, is then obtained by extrapolating R_0 to the long-chain limit. Because a has not been available to previous CL-FTSs, results have been expressed in terms of the bare statistical segment length, a_b, of an isolated polymer, which introduces inaccuracies even though the simulation method itself is inherently exact. In a few cases, a has been estimated by a weak-field approximation, but its accuracy remains uncertain. This study focuses on the fluctuation correction, a-a_b, for compressible melts of discrete Gaussian chains with finite-range interactions and compares it to the weak-field approximation. The approximation underestimates the fluctuation correction by up to 20%, but this is not particularly serious given that the correction itself is a small effect. Notably, our technique for evaluating R_0 can be generalized to any single-chain observable, which allows access to all the intramolecular correlations.