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arXiv · 1212.5231

Stability of complex Langevin dynamics in effective models

Gert Aarts·Frank A. James·Jan M. Pawlowski·Erhard Seiler·Denes Sexty·Ion-Olimpiu Stamatescu
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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.

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Gert Aarts, Frank A. James, Jan M. Pawlowski, Erhard Seiler, Denes Sexty, Ion-Olimpiu Stamatescu. 2013-02-28. Stability of complex Langevin dynamics in effective models. https://doi.org/10.1007/jhep03(2013)073

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