2017/12/19 by Jacques Bloch, J. Bloch, Jonas Glesaaen +4
Mathematics · Physics and Astronomy · #Applied mathematics #Convergence (economics) #Eigenvalues and eigenvectors #Langevin dynamics #Materials science #Mathematics #Matrix (chemical analysis) #Particle physics #Phase transition #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Quark #Random matrix #Representation (politics) #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #hep-lat #hep-ph #nucl-th
paper · pdf · doi:10.1007/jhep03(2018)015
33 pages, 22 figures
arxiv created 2017/12/19 · openalex publication_date 2018/03/01 · arxiv updated 2018/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A bstract In this paper we test the complex Langevin algorithm for numerical simulations of a random matrix model of QCD with a first order phase transition to a phase of finite baryon density. We observe that a naive implementation of the algorithm leads to phase quenched results, which were also derived analytically in this article. We test several fixes for the convergence issues of the algorithm, in particular the method of gauge cooling, the shifted representation, the deformation technique and reweighted complex Langevin, but only the latter method reproduces the correct analytical results in the region where the quark mass is inside the domain of the eigenvalues. In order to shed more light on the issues of the methods we also apply them to a similar random matrix model with a milder sign problem and no phase transition, and in that case gauge cooling solves the convergence problems as was shown before in the literature.