lead to sizable corrections to mean-field theory is restricted to the vicinity of the critical point. Secondly, in low-dimensional systems fluctuations are important down to lower temperatures, where they can lead to the breakdown of true long-range order [@MerminWagner-PRL1966; @Hohenberg-PR1967]. At zero temperature, deep inside the ordered phase, (quantum) fluctuations are expected to have severe consequences only for one-dimensional systems, while they are small in spatial dimensions $d\geq2$. Here we consider different fluctuations with characteristic length scales shorter than $\xi$.

To self-consistently check the validity of a mean-field theory, we determine fluctuation corrections to the zero-temperature gap equation and compare the resulting contributions due to fluctuations to the mean-field terms. This approach was put forward in the context of superconductivity by Kos, Millis, and Larkin [@KosMillisLarkin-PRB2004]; and their self-consistent calculation of corrections to the BCS gap equation indeed showed that the BCS mean-field theory is justified. This analysis for $s$-wave superconductors can be extended to charged superconductors [@FischerEtAl2017] as well as anisotropic superconductors [@ParamekantiEtAl-PRB2000; @BarlasVarma-PRB2013; @Hoyer-Thesis2017], resulting in the conclusion that fluctuation corrections to the zero-temperature gap equation are generally negligible for superconductors. Remarkably, this is due to an exact cancellation of individually large contributions that can be assigned to 