PoS - Proceedings of Science
Volume 334 - The 36th Annual International Symposium on Lattice Field Theory (LATTICE2018) - Theoretical Developments
Critical behavior of the hopping expansion from the Functional Renormalization Group
R. Banerjee
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Published on: May 29, 2019
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 $\phi^4_4$ theory and its $\phi_3^4$ counterpart.
DOI: https://doi.org/10.22323/1.334.0249
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