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Optimization and Stabilization of Functional Renormalization Group Flows

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arxiv 2401.12854 v2 pith:ZVBFJZ6Y submitted 2024-01-23 hep-ph hep-thnucl-th

Niklas Zorbach , Jonas Stoll , Jens Braun This is my paper · ORCID
classification hep-phhep-thnucl-th
keywords flowsgrouprenormalizationorderprinciplefunctionaloptimizationregulators
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We revisit optimization of functional renormalization group flows by analyzing regularized loop integrals. This leads us to a principle, the Principle of Strongest Singularity, and a corresponding order relation which allows to order existing regularization schemes with respect to the stability of renormalization group flows. Moreover, the order relation can be used to construct new regulators in a systematic fashion. For studies of critical behavior, which require to follow renormalization group flows down to the deep infrared regime, such new regulators may turn out to be particularly useful. The general application of this principle is demonstrated with the aid of a scalar field theory which is solved over a wide range of scales with novel methods borrowed from numerical fluid dynamics.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Functional renormalization of QCD in $1 + 1$ dimensions: four-fermion interactions from quark-gluon dynamics

    hep-ph 2024-12 conditional novelty 7.0 of 10

    First functional renormalization group study of two-dimensional QCD with a mass-like regulator, producing flow equations for the gauge coupling, quark mass, and a Fierz-complete set of four-fermion interactions.

  2. Multiloop functional renormalization group from single bosons

    cond-mat.str-el 2025-12 conditional novelty 6.0 of 10

    A multiloop functional renormalization group in the single-boson-exchange representation reproduces parquet-approximation results for the 2D Hubbard model within a few percent when multi-boson rest functions are neglected.

  3. Functional Renormalization Group meets Computational Fluid Dynamics: RG flows in a multi-dimensional field space

    cond-mat.stat-mech 2024-12 conditional novelty 6.0 of 10

    A two-dimensional Kurganov-Tadmor finite-volume scheme accurately solves FRG flow equations for effective potentials in multi-dimensional field space, benchmarked against exact zero-dimensional path integrals and appl...

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