view is the investigation of the instability of the disordered state. For the density-wave systems discussed here, the latter can be performed using a renormalization group (RG) treatment [@Shankar-RevModPhys1994]. Consistent with our results, channel interference of the RG analysis suggests corrections to mean-field behavior. This is discussed briefly in Sec. \[sec:rg\] and Appendix \[app:two-band\]. The appeal of our approach is, however, that it offers a simple physical picture for the role of order-parameter fluctuations: amplitude variations suppress the order parameter compared to its mean-field value, whereas phase fluctuations enhance it.

In this paper, we address the role of fluctuations for mean-field theories of commensurate density-wave order in systems with perfect nesting: We provide a self-consistent calculation of Gaussian fluctuation corrections to the zero-temperature gap equation. We come to the conclusion that, in contrast to BCS theory, these mean-field theories are not justified since sizable fluctuation corrections are inherent to these theories. The mean-field approach is then only valid if the number of amplitude and phase fluctuations is the same. Thus the mean-field approach is neither valid for Heisenberg SDWs nor for CDWs. The only exception is spin-density wave order of XY spins, where longitudinal and transverse fluctuation contributions cancel exactly 