Beyond the Thouless energy

Abstract

The distribution and the correlations of the small eigenvalues of the Dirac operator are described by random matrix theory (RMT) up to the Thouless energy $E_c\propto 1/\sqrt{V}$, where $V$ is the physical volume. For somewhat larger energies, the same quantities can be described by chiral perturbation theory (chPT). For most quantities there is an intermediate energy regime, roughly $1/V<E<1/\sqrt{V}$, where the results of RMT and chPT agree with each other. We test these predictions by constructing the connected and disconnected scalar susceptibilities from Dirac spectra obtained in quenched SU(2) and SU(3) simulations with staggered fermions for a variety of lattice sizes and coupling constants. In deriving the predictions of chPT, it is important to take into account only those symmetries which are exactly realized on the lattice.

LATTICE99(Theoretical Developments), 3 pages, 3 figures, typo in Ref. [10] corrected

References in corpus (7)

• The Microscopic Spectral Density of the QCD Dirac Operator
• From chiral Random Matrix Theory to chiral Perturbation Theory
• Thouless Energy and Correlations of QCD Dirac Eigenvalues
• Chiral Disorder in QCD
• Thouless Energy and Correlations of QCD Dirac Eigenvalues
• Small eigenvalues of the SU(3) Dirac operator on the lattice and in Random Matrix Theory
• Crossover to Non-universal Microscopic Spectral Fluctuations in Lattice Gauge Theory

Cited by in corpus (1)

• Spectrum of the SU(3) Dirac operator on the lattice: Transition from random matrix theory to chiral perturbation theory