  A nonconventional renormalization-group (RG) treatment close to and below
four dimensions is used to explore, in a unified and systematic way, the
low-temperature properties of a wide class of systems in the influence domain
of their quantum critical point. The approach consists in a preliminary
averaging over quantum degrees of freedom and a successive employment of the
Wilsonian RG transformation to treat the resulting effective classical
Ginzburg-Landau free energy functional. This allows us to perform a detailed
study of criticality of the quantum systems under study. The emergent physics
agrees, in many aspects, with the known quantum critical scenario. However, a
richer structure of the phase diagram appears with additional crossovers which
are not captured by the traditional RG studies. In addition, in spite of the
intrinsically static nature of our theory, predictions about the dynamical
critical exponent, which parametrizes the link between statics and dynamics
close to a continuous phase transition, are consistently derived from our
static results.
