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We study the impact of quantum and thermal fluctuations on properties ofquantum phase transitions occurring in systems of itinerant fermions with mainfocus on the order of these transitions. Our approach is based on a set of flowequations derived within the functional renormalization group framework, inwhich the order parameter is retained as the only degree of freedom, and wherethe effective potential is parametrized with a phi^6 form allowing for bothfirst and second order scenarios. We find a tendency to turn the first ordertransitions within the bare model into second order transitions upon accountingfor the order parameter fluctuations. We compute the first and second orderphase boundary lines T_c as a function of a non-thermal control parameter a_2in the vicinity of a quantum phase transition. We analyze crossovers of theshift exponent psi governing the shape of the T_c line when the system is tunedclose to a quantum tricritical scenario, where a second order phase transitionline terminates at a quantum tricritical point.

Renormalized phi^6 model for quantum phase transitions in systems of itinerant fermions