  An approach to studying lattice gauge models in the weak coupling region is
proposed. Conceptually, it is based on the crucial role of the original Z(N)
symmetry and the invariant gauge group measure. As an example, we calculate an
effective model from the compact Wilson formulation of the SU(2) gauge theory
in $d=3D3$ dimensions at zero temperature. Confining properties and phase
structure of the effective model are studied in details.
