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Stability of complex Langevin dynamics in effective models

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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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Authors and Affiliations

  1. Department of Physics, College of Science, Swansea University, Swansea, United Kingdom

    Gert Aarts

  2. Institute for Theoretical Physics, Universität Regensburg, Regensburg, Germany

    Frank A. James

  3. Institut für Theoretische Physik, Universität Heidelberg, Heidelberg, Germany

    Jan M. Pawlowski, Dénes Sexty & Ion-Olimpiu Stamatescu

  4. Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München, Germany

    Erhard Seiler

  5. FEST, Heidelberg, Germany

    Ion-Olimpiu Stamatescu

Authors
  1. Gert Aarts
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  2. Frank A. James
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  3. Jan M. Pawlowski
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  4. Erhard Seiler
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  5. Dénes Sexty
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  6. Ion-Olimpiu Stamatescu
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Correspondence to Gert Aarts.

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ArXiv ePrint: 1212.5231

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Aarts, G., James, F.A., Pawlowski, J.M. et al. Stability of complex Langevin dynamics in effective models. J. High Energ. Phys. 2013, 73 (2013). https://doi.org/10.1007/JHEP03(2013)073

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  • DOI: https://doi.org/10.1007/JHEP03(2013)073

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