Deconfinement phase transition in gauge theories with discrete symmetry

We study the deconfinement phase transitions in three-dimensional Z(N) gauge theory at finite temperature using formulation of the model on anisotropic lattice. In the strong coupling limit with respect to the spatial coupling the model can be reduced to a generalized version of 2D Z(N) spin model. When N is sufficiently large this model has two phase transitions, one of which is of the Berezinskii-Kosterlitz-Thouless type and belongs to the U(1) universality class. We advance analytical arguments that the deconfinement phase transition in 3D Z(N) gauge model also is in the universality class of the two-dimensional XY model.