Critical behavior of the hopping expansion from the Functional Renormalization Group

Abstract

A lattice version of the widely used Functional Renormalization Group (FRG) for the Legendre effective action is solved - in principle exactly - in terms of graph rules for the linked cluster expansion. Conversely, the FRG induces nonlinear flow equations governing suitable resummations of the graph expansion. The (finite) radius of convergence determining criticality can then be efficiently computed as the unstable manifold of a Gaussian or non-Gaussian fixed point of the FRG flow. The correspondence is tested on the critical line of the Lüscher-Weisz solution of the ${\varphi }_4^4$ theory and its ${\varphi }_3^4$ counterpart.

Comments: 1+6 pages, proceedings for the 36th International Symposium on Lattice Field Theory (22-28 July 2018)