Spectral properties of the Landau gauge Faddeev-Popov operator in lattice gluodynamics

Abstract

Recently we reported on the infrared behavior of the Landau gauge gluon and ghost dressing functions in SU(3) Wilson lattice gluodynamics with special emphasis on the Gribov problem. Here we add an investigation of the spectral properties of the Faddeev-Popov operator at $\beta$=5.8 and 6.2 for lattice sizes 12^4, 16^4 and 24^4. The larger the volume the more of its eigenvalues are found accumulated close to zero. Using the eigenmodes for the spectral representation it turns out that for our smallest lattice O(200) eigenmodes are sufficient to saturate the ghost propagator at lowest momentum. We associate exceptionally large values of the ghost propagator to extraordinary contributions of low-lying eigenmodes.