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We extend the Hertz-Millis theory of quantum phase transitions in itinerantelectron systems to phases with broken discrete symmetry. Using a set ofcoupled flow equations derived within the functional renormalization groupframework, we compute the second order phase transition line T_c(delta), withdelta a non-thermal control parameter, near a quantum critical point. Weanalyze the interplay and relative importance of quantum and classicalfluctuations at different energy scales, and we compare the Ginzburgtemperature T_G to the transition temperature T_c, the latter being associatedwith a non-Gaussian fixed-point.

Renormalization group for phases with broken discrete symmetry near quantum critical points