  We study the impact of quantum and thermal fluctuations on properties of
quantum phase transitions occurring in systems of itinerant fermions with main
focus on the order of these transitions. Our approach is based on a set of flow
equations derived within the functional renormalization group framework, in
which the order parameter is retained as the only degree of freedom, and where
the effective potential is parametrized with a phi^6 form allowing for both
first and second order scenarios. We find a tendency to turn the first order
transitions within the bare model into second order transitions upon accounting
for the order parameter fluctuations. We compute the first and second order
phase boundary lines T_c as a function of a non-thermal control parameter a_2
in the vicinity of a quantum phase transition. We analyze crossovers of the
shift exponent psi governing the shape of the T_c line when the system is tuned
close to a quantum tricritical scenario, where a second order phase transition
line terminates at a quantum tricritical point.
