  Adding separate chemical potentials lambda and gamma for Z2 monopoles and
vortices respectively in the Villain form of the mixed fundamental-adjoint
action for the SU(2) lattice gauge theory, we investigate their role in the
interplay between the deconfinement and bulk phase transitions using Monte
Carlo techniques. Setting lambda to be nonzero, we find that the line of
deconfinement transitions is shifted in the coupling plane but it behaves
curiously also like the bulk transition line for large enough adjoint coupling,
as for lambda=0. In a narrow range of couplings, however, we find separate
deconfinement and bulk phase transitions on the same lattice for nonzero and
large lambda, suggesting the two to be indeed coincident in the region where a
first order deconfinement phase transition is seen. In the limit of large
lambda and gamma, we obtain only lines of second order deconfinement phase
transitions, as expected from universality.
