  Phase transitions in zero-temperature 3D Z(N) lattice gauge theories are
studied. We use a cluster algorithm defined for the dual formulation of the
models. We also attempt to explain the nature of the intermediate continuously
symmetric phase, which appears for N>5. The critical indices are calculated.
The results obtained are used to study the scaling of critical points with N,
as well as the scaling of finite-temperature critical points with the lattice
size in the time direction, $N_t$.
