UV/IR Mixing In Non-Fermi Liquids: Higher-Loop Corrections In Different Energy Ranges

We revisit the Ising-nematic quantum critical point with an $m$-dimensional Fermi surface by applying a dimensional regularization scheme, introduced in Phys. Rev. B 92, 035141 (2015). We compute the contribution from two-loop and three-loop diagrams in the intermediate energy range controlled by a crossover scale. We find that for $m=2$, the corrections continue to be one-loop exact for both the infrared and intermediate energy regimes.