1997/04/30 by M. A. Halasz, M. Á. Halász, James C. Osborn +2 · 3 citations
Mathematics · Physics and Astronomy · #Complex plane #Eigenvalues and eigenvectors #Fermion #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Random Matrices and Applications #Random matrix #Resolvent #Theoretical and Computational Physics #Thermodynamic limit #cond-mat #hep-lat
paper · pdf · doi:10.1103/physrevd.56.7059
published as Phys.Rev.D56:7059-7062,1997 · 4 pages, 2 figures, Latex, modified the introduction
arxiv created 1997/07/07 · openalex publication_date 1997/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce three universality classes of chiral random matrix ensembles with a nonzero chemical potential and real, complex or quaternion real matrix elements. In the thermodynamic limit we find that the distribution of the eigenvalues in the complex plane does not depend on the Dyson index, and is given by the solution proposed by Stephanov. For a finite number of degrees of freedom, N, we find an accumulation of eigenvalues on the imaginary axis for real matrices, whereas for quaternion real matrices we find a depletion of eigenvalues in this domain. This effect is of order 1/√(N). In particular for the real case the resolvent shows a discontinuity of order 1/√(N). These results are in agreement with lattice QCD simulations with staggered fermions and recent instanton liquid simulations both for two colors and a nonzero chemical potential.