Large Orders and Strong-Coupling Limit in Functional Renormalization

TL;DR

This paper analyzes the large-order behavior of the functional renormalization group, establishing Borel-summability and universality in the strong-coupling limit, with implications for disordered elastic systems.

Contribution

It demonstrates Borel-summability for a class of models and shows universality of fixed points in the strong-coupling limit within the FRG framework.

Findings

Borel-summability established for zero-dimensional models.

All microscopic disorders flow to a universal fixed point.

Results are relevant for disordered elastic systems.

Abstract

We study the large-order behavior of the functional renormalization group (FRG). For a model in dimension zero, we establish Borel-summability for a large class of microscopic couplings. Writing the derivatives of FRG as contour integrals, we express the Borel-transform as well as the original series as integrals. Taking the strong-coupling limit in this representation, we show that all short-ranged microscopic disorders flow to the same universal fixed point. Our results are relevant for FRG in disordered elastic systems.