Random Matrix Model of QCD at Finite Density and the Nature of the Quenched Limit

1996/04/30 by Mikhail Stephanov, M. A. Stephanov · 367 citations
Mathematics · Physics and Astronomy · #Eigenvalues and eigenvectors #Limit (mathematics) #Materials science #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Particle physics #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chaos and dynamical systems #Quantum chromodynamics #Quantum electrodynamics #Quantum mechanics #Random matrix #Statistical physics #Theoretical and Computational Physics #cond-mat #hep-lat #hep-ph #hep-th

paper · pdf · doi:10.1103/physrevlett.76.4472

published in Physical Review Letters 76(24), 4472-4475 (American Physical Society) · 9 pages, revtex3.0, 4 epsf figures. Packed by "uufiles" script. Revised version (PRL): minor changes

arxiv created 1996/05/14 · openalex publication_date 1996/06/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We use a random matrix model to study chiral symmetry breaking in QCD at finite chemical potential \ensuremathμ. We solve the model and compute the eigenvalue density of the Dirac matrix on a complex plane. A naive ``replica trick'' fails for \ensuremathμ\ensuremath≠0; we find that quenched QCD is not a simple n\ensuremath→0 limit of QCD with n quarks. It is the limit of a theory with 2n quarks: n quarks with original action and n quarks with conjugate action. The results agree with earlier studies of lattice QCD at \ensuremathμ\ensuremath≠0 and provide a simple analytical explanation of a long-standing puzzle.

Citations

• Quenched QCD at finite density: g = 1 and g = ∞

Cited by

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