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Numerical RG-time integration of the effective potential: Analysis and Benchmark

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arxiv 2302.04736 v1 pith:DXP5RR6Y submitted 2023-02-09 hep-th cond-mat.stat-mechphysics.comp-ph

Friederike Ihssen , Franz R. Sattler , Nicolas Wink This is my paper · ORCID
classification hep-thcond-mat.stat-mechphysics.comp-ph
keywords differentintegrationmethodspotentialrg-timecombinationdiscreteeffective
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abstract

We investigate the RG-time integration of the effective potential in the functional renormalization group in the presence of spontaneous symmetry breaking and its subsequent convexity restoration on the example of a scalar theory in $d=3$. The features of this setup are common to many physical models and our results are, therefore, directly applicable to a variety of situations. We provide exhaustive work-precision benchmarks and numerical stability analyses by considering the combination of different discrete formulations of the flow equation and a large collection of different algorithms. The results are explained by using the different components entering the RG-time integration process and the eigenvalue structure of the discrete system. Particularly, the combination of Rosenbrock methods, implicit multistep methods or certain (diagonally) implicit Runge-Kutta methods with exact or autodiff Jacobians proves to be very potent. Furthermore, a reformulation in a logarithmic variable circumvents issues related to the singularity bound in the flat regime of the potential.

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Cited by 4 Pith papers

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

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    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

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    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

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