Three-dimensional lattice <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>SU</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math> gauge theories with multiflavor scalar fields in the adjoint representation

We consider three-dimensional lattice SU($N_c$) gauge theories with multiflavor ($N_f>1$) scalar fields in the adjoint representation. investigate their phase diagram, identify different Higgs phases gauge-symmetry pattern, and determine nature of transition lines. In particular, we study role played by quartic potential gauge-group representation determining global symmetry-breaking patterns characterizing transitions. The general arguments are confirmed numerical analyses Monte Carlo results for two representative models that expected to have qualitatively diagrams phases. model $N_c = 3$, $N_f=2$ $N_c=2$, $N_f= 4$. This second case is interesting phenomenologically describe some features cuprate superconductors.