Non-trivial Fixed Point of a Fermionic Theory, II: Anomalous Exponent and Scaling Operators.

We consider the Renormalization Group (RG) fixed-point theory associated with a fermionic model in with fractional kinetic term, whose scaling dimension is fixed so that the quartic interaction is weakly relevant in the RG sense. The model is defined in terms of a Grassmann functional integral with interaction , solving a fixed-point RG equation in the presence of external fields, and a fixed ultraviolet cutoff. We define and construct the field and density scale-invariant response functions, and prove that the critical exponent of the former is the naive one, while that of the latter is anomalous and analytic. We construct the corresponding (almost-)scaling operators, whose two point correlations are scale-invariant up to a remainder term, which decays like a stretched exponential at distances larger than the inverse of the ultraviolet cutoff. Our proof is based on constructive RG methods and, specifically, on a convergent tree expansion for the generating function of correlations, which generalizes the approach developed by three of the authors in a previous publication (Giuliani et al. in JHEP 01:026, 2021. 10.1007/JHEP01(2021)026. arXiv:2008.04361 [hep-th]).