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 Nf flavors, characterized by a non-Abelian SU(Nc) gauge symmetry. For Nf≥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) φ4 approach based on a gauge-invariant order parameter. Their predictions are compared with simulation results for Nf=2, 3 and Nc=2-4. The LGW approach turns out to provide the correct picture of the critical behavior at the transitions between the two phases.