  Lattice Monte Carlo simulations are performed for the SU(2) Yang Mills gauge
theory in the presence of an Abelian background with external sources to obtain
information on the effective potential. The goal is to investigate the lowest
Landau mode that, in the continuum one-loop effective potential, is the crucial
mode for instability. It is shown that also in the lattice formulation this
lowest Landau mode plays a very peculiar role, and it is important for the
understanding of the vacuum properties.
