Scaling Properties of the Probability Distribution of Lattice Gribov Copies

We study the problem of the Landau gauge fixing in the case of the SU(2) lattice gauge theory. We show that the probability to find a lattice Gribov copy increases considerably when the physical size of the lattice exceeds some critical value $\approx2.75/\sqrt{\sigma}$, almost independent of the lattice spacing. The impact of the choice of the copy on Green functions is presented. We confirm that the ghost propagator depends on the choice of the copy whereas the gluon propagator is insensitive to it (within present statistical errors). The gluonic three-point functions are also insensitive to it. Finally we show that gauge copies which have the same value of the minimisation functional ($\int d^4x (A^a_\mu)^2$) are equivalent, up to a global gauge transformation, and yield the same Green functions.