  We study the vacuum behavior at one loop level in extended Higgs sectors with
two doublets (2HDM), where $U(1)$ and $Z_{2}$ symmetries are considered to
protect the $CP$ symmetry in the Higgs potential and to avoid Flavor Changing
Neutral Currents at tree level in the Yukawa sector. In the Inert Higgs Model
case, a detailed comparison is made between both models by using the energy
evolution of couplings, which should satisfy energy scale dependent relations
deduced for minima and stationary points of the Higgs potential at tree level.
Besides, perturbative unitarity constraints at tree level are considered to
generate the allowed parameter space compatible with perturbativity (absence of
Landau poles). Our studies illustrate exclusion regions for Higgs masses and
other combinations of couplings in the scalar sector, in particular for
splittings of mass square for neutral scalars $A^{0}$ and $H^{0}$, as well as
the difference between the sum of these and the charged Higgs mass square. From
the vacuum stability for inert-2HDM at the tree and one loop levels, analyses
lead us to find out new hierarchical structures for scalar masses. To complete
vacuum studies on the Inert model, and based on reparameterization invariance
of the Higgs potential, we compute original discriminants that allow ensuring
the presence of a global electroweak minimum at tree level. Moreover, the
behavior in high energy scales drives out analyzing criticality phenomena for
the additional parameters of extended Higgs sectors. Finally, and using the
consistency with the electroweak precision analyses of oblique parameters, we
describe several implications from different regimes of the inert model on
charged and pseudoscalar Higgs searches.
