Critical behavior of the hopping expansion from the Functional Renormalization Group

Understand

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 L\"{u}scher-Weisz solution of the $\phi^4_4$ theory and its $\phi_3^4$ counterpart.