  We study the nature of the phase diagram of three-dimensional lattice models
in the presence of nonabelian gauge symmetries. In particular, we consider a
paradigmatic model for the Higgs mechanism, lattice scalar chromodynamics with
N_f flavors, characterized by a nonabelian SU(N_c) gauge symmetry. For N_f>1
(multiflavor case), it presents two phases separated by a transition line where
a gauge-invariant order parameter condenses, being associated with the breaking
of the residual global symmetry after gauging. The nature of the phase
transition line is discussed within two field-theoretical approaches, the
continuum scalar chromodynamics and the Landau-Ginzburg- Wilson (LGW) Phi4
approach based on a gauge-invariant order parameter. Their predictions are
compared with simulation results for N_f=2, 3 and N_c = 2, 3, and 4. The LGW
approach turns out to provide the correct picture of the critical behavior,
unlike continuum scalar chromodynamics.
