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Local Discontinuous Galerkin for the Functional Renormalisation Group

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arxiv 2207.12266 v2 pith:SDSBAA3H submitted 2022-07-25 hep-th hep-ph

Friederike Ihssen , Jan M. Pawlowski , Franz R. Sattler , Nicolas Wink This is my paper · ORCID
classification hep-thhep-ph
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abstract

We apply the Local Discontinuous Galerkin discretisation to flow equations of the O(N)-model in the Local Potential Approximation. The improved stability is directly observed by solving the flow equation for various $N$ and space-time dimensions $d$. A particular focus of this work is the numerical discretisation and its implementation. The code is publicly available, and is explained in detail here. It is realised as a module within the high performance PDE framework DUNE.

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Cited by 4 Pith papers

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

  1. Quantum critical fan and emergent relativistic symmetry of two-dimensional Dirac semimetals

    cond-mat.str-el 2026-07 conditional novelty 6.0 of 10

    A functional-RG calculation maps the chiral Ising Gross-Neveu-Yukawa phase diagram, confirming emergent relativistic symmetry at the quantum critical point and 2D Ising behavior at the finite-temperature transition.

  2. 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...

  3. DiFfRG: A Discretisation Framework for functional Renormalisation Group flows

    hep-ph 2024-12 conditional novelty 6.0 of 10

    DiFfRG provides a general, code-generated numerical toolkit for fRG flows, demonstrated on O(N), Quark-Meson, Yang-Mills, and four-fermion systems.

  4. Critical scaling for spectral functions

    hep-th 2025-06 conditional novelty 5.0 of 10

    A spectral renormalisation group computation extracts the anomalous dimension eta ~ 0.1 for 2+1-dimensional phi^4 theory in the scaling regime, within a truncated approximation.

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