Stability of complex Langevin dynamics in effective models
Abstract
The sign problem at nonzero chemical potential prohibits the use of importance sampling in lattice simulations. Since complex Langevin dynamics does not rely on importance sampling, it provides a potential solution. Recently it was shown that complex Langevin dynamics fails in the disordered phase in the case of the three-dimensional XY model, while it appears to work in the entire phase diagram in the case of the three-dimensional SU(3) spin model. Here we analyse this difference and argue that it is due to the presence of the nontrivial Haar measure in the SU(3) case, which has a stabilizing effect on the complexified dynamics. The freedom to modify and stabilize the complex Langevin process is discussed in some detail.
Keywords
Cite
@article{arxiv.1212.5231,
title = {Stability of complex Langevin dynamics in effective models},
author = {Gert Aarts and Frank A. James and Jan M. Pawlowski and Erhard Seiler and Denes Sexty and Ion-Olimpiu Stamatescu},
journal= {arXiv preprint arXiv:1212.5231},
year = {2015}
}
Comments
29 pages, several eps figures; minor clarifications added, to appear in JHEP