Numerical Study of the Fundamental Modular Region in the Minimal Landau Gauge

Details Numerical Study of the Fundamental Modular Region in the Minimal Landau Gauge Numerical Study of the Fundamental Modular Region in the Minimal Landau Gauge

1997-11-13

arxiv.org/abs/hep-lat/9711024v2

Nucl.Phys. B521 (1998) 365-379

Physics

High Energy Physics

High Energy Physics - Lattice

17 pages, including two figures; latex style has been corrected

Scientific paper

10.1016/S0550-3213(98)00235-1

We study numerically the so-called fundamental modular region Lambda, 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 Lambda. Simulations are done at four different values of the coupling: beta = 0, 0.8, 1.6, 2.7, and for volumes up to 16^4. We find that typical (thermalized and gauge-fixed) configurations, including those belonging to the region Lambda, lie very close to the Gribov horizon $\partial \Omega$, and are characterized, in the limit of large lattice volume, by a negative-definite horizon tensor.

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