Numerical study of the fundamental modular region in the minimal Landau gauge Original Research Article

We study numerically the so-called fundamental modular region Λ, a region free of Gribov copies, in the minimal Landau gauge for pure SU(2) lattice gauge theory. To this end we evaluate the influence of Gribov copies on several quantities — such as the smallest eigenvalue of the Faddeev-Popov matrix, the third and the fourth derivatives of the minimizing function, and the so-called horizon function — which are used to characterize the region Λ. Simulations are done at four different values of the coupling: β = 0, 0.8, 1.6, 2.7, and for volumes up to 164. We find that typical (thermalized and gauge-fixed) configurations, including those belonging to the region Λ, lie very close to the Gribov horizon ∂ω, and are characterized, in the limit of large lattice volume, by a negative-definite horizon tensor.