  Universal features of continuous phase transitions can be investigated by
studying the $\phi^4$ field theory with the corresponding global symmetry
breaking pattern. When gauge symmetries are present, the same technique is
usually applied to a gauge-invariant order parameter field, as in the
Pisarski-Wilczek analysis of the QCD chiral phase transition. Gauge fields are
thus assumed to be irrelevant in the effective critical model, a fact that is
however far from trivial. We will investigate the validity of this approach
using three-dimensional scalar lattice models with non-abelian global and local
symmetries, for which critical exponents and scaling functions can be
numerically determined with high accuracy.
