Exact solutions and residual regulator dependence in functional renormalisation group flows

We construct exact solutions to the functional renormalisation group equation of the O(N) model and the Gross-Neveu model at large N for 2 < d < 4, without specifying the form of the regulator. This allows to investigate which quantities are independent of the choice of regulator without being plagued by truncation artefacts. We find that only universal quantities, like critical exponents, and qualitative features, like the existence of a finite vacuum expectation value, are regulator-independent, whereas values of coupling constants are generically arbitrary. We also provide a general algorithm to construct a concrete operator basis for truncations in the derivative expansion and the Blaizot-Mendez-Wschebor scheme.

Automated summary

We investigated exact solutions to the functional renormalisation group equation of the O(N) model and the Gross-Neveu model at large N for 2 < d < 4 without specifying the form of the regulator. It was found that only universal quantities and qualitative features are regulator-independent, while coupling constants are typically arbitrary. A general algorithm was also provided to construct a concrete operator basis for truncations in the derivative expansion and the Blaizot-Mendez-Wschebor scheme.