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) Φ^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.