Eigenvalue Distributions of the QCD Dirac Operator

Abstract

We compute by Monte Carlo methods the individual distributions of the $k$th smallest Dirac operator eigenvalues in QCD, and compare them with recent analytical predictions. We do this for both massless and massive quarks in an SU(3) gauge theory with staggered fermions. Very precise agreement is found in all cases. As a simple by-product we also extract the microscopic spectral density of the Dirac operator in SU(3) gauge theory with dynamical massive fermions for $N_f=1$ and 2, and obtain high-accuracy agreement with analytical expressions.

LaTeX, 8 pages, 9 postscript figures. Very minor corrections

References in corpus (9)

• The Spectral Density of the QCD Dirac Operator and Patterns of Chiral Symmetry Breaking
• Universal Scaling of the Chiral Condensate in Finite-Volume Gauge Theories
• Spectra of massive and massless QCD Dirac operators: A novel link
• Spectral Sum Rules of the Dirac operator and Partially Quenched Chiral Condensates
• Topology and the Dirac Operator Spectrum in Finite-Volume Gauge Theories
• Partially Quenched Chiral Condensates from the Replica Method
• Staggered Fermions and Gauge Field Topology
• On Finite-Volume Gauge Theory Partition Functions
• Effects of Topology in the Dirac Spectrum of Staggered Fermions

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