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

We extend the Hertz-Millis theory of quantum phase transitions in itinerant electron systems to phases with broken discrete symmetry. By using a set of coupled flow equations derived within the functional renormalization group framework, we compute the second order phase, transition line T-c(delta), where delta is a nonthermal control parameter, near a quantum critical point. We analyze the interplay and relative importance of quantum and classical fluctuations at different energy scales, and we compare the Ginzburg temperature T-G to the transition temperature T-c, the latter being associated with a non-Gaussian fixed point.