Effect of a nonzero temperature on quantum critical points in itinerant fermion systems

I reexamine the work of Hertz on quantum phase transitions in itinerant fermion systems. I determine when it is permissible to integrate out the fermions and analyze the critical phenomena via an effective bosonic theory in which only fluctuations of the ordering field are explicitly retained. By solving appropriate scaling equations I obtain the different regimes of behavior of the correlation length and free energy in the disordered phase of the effective bosonic theory. The results in many cases differ from those of Hertz, but make contact with more recent work on the dilute Bose gas. I briefly discuss the relevance of the results to heavy-fermion materials.