Phase Diagram, Symmetry Breaking, and Critical Behavior of Three-Dimensional Lattice Multiflavor Scalar Chromodynamics

We study the nature of the phase diagram of three-dimensional lattice models in the presence of non-Abelian gauge symmetries. In particular, we consider a paradigmatic model for the Higgs mechanism, lattice scalar chromodynamics with N-f flavors, characterized by a non-Abelian SU(N-c) gauge symmetry. For N-f >= 2 (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) Phi(4) approach based on a gauge-invariant order parameter. Their predictions are compared with simulation results for N-f = 2, 3 and N-c = 2-4. The LGW approach turns out to provide the correct picture of the critical behavior at the transitions between the two phases.