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Status of Complex Langevin

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arxiv 1708.08254 v3 pith:HFHQGOOJ submitted 2017-08-28 hep-lat

classification hep-lat
keywords complexlangevinmethodstatusactionapplicationbaryonicchemical
verification ladder T0 review T1 audit T2 compute T3 formal

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I review the status of the Complex Langevin method, which was invented to make simulations of models with complex action feasible. I discuss the mathematical justification of the procedure, as well as its limitations and open questions. Various pragmatic measures for dealing with the existing problems are described. Finally I report on the progress in the application of the method to QCD, with the goal of determining the phase diagram of QCD as a function of temperature and baryonic chemical potential.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Phase structure of the 1+1 dimensional massive Thirring model from matrix product states

    hep-lat 2019-08 conditional novelty 5.0 of 10

    The 1+1 dimensional massive Thirring model has a conformal critical phase and a gapped phase separated by a Berezinskii-Kosterlitz-Thouless transition, as shown by tensor-network simulations.

  2. Thermodynamic Diagnostics for Complex Langevin Simulations: The Role of Configurational Temperature

    hep-lat 2025-09 conditional novelty 4.0 of 10

    Configurational temperature from action gradients and Hessians offers a sensitive new correctness diagnostic for complex Langevin simulations, reproducing input temperature to 0.2-3% in 1D PT-symmetric models.

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