Abstract
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.
Highlights
Local gauge symmetries are key features of theories describing fundamental interactions [1] and emerging phenomena in condensed matter physics [2]
We study the nature of the phase diagram of three-dimensional lattice models in the presence of nonAbelian gauge symmetries
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
Summary
Variance with systems that only have global symmetries, there is not a unique natural effective theory for the transition. One may consider a Landau-Ginzburg-Wilson (LGW) Φ4 theory based on a gauge-invariant order-parameter field with the global symmetry of the model [15,23]. While in the first approach the gauge symmetry is still present in the effective model, in the second one, gauge invariance does not play a particular role besides fixing the order parameter. The natural order parameter is the operator Qfxg defined in Eq (3) This is a nontrivial assumption, as it postulates that gauge fields do not play a relevant role in the effective theory of the critical modes. Summarizing, the LGW approach based on a gaugeinvariant order parameter predicts that continuous transitions only occur for Nf 1⁄4 2. GðpÞ x eip·xGðxÞ and pm 1⁄4 ð2π=L; 0; 0Þ
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