Third Order Renormalization Group applied to the attractive one-dimensional Fermi Gas

摘要

We consider a Callan-Symanzik and a Wilson Renormalization Group approach tothe infrared problem for interacting fermions in one dimension withbackscattering. We compute the third order (two-loop) approximation of the betafunction using both methods and compare it with the well known multiplicativeGell-Mann Low approach. We point out a previously unnoticed qualitativedependence of the third order fixed point on an arbitrary dimensionlessparameter, which strongly suggest the spurious nature of the fixed point.