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arXiv · 2302.04736

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

Friederike Ihssen·Franz R. Sattler·Nicolas Wink
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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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Friederike Ihssen, Franz R. Sattler, Nicolas Wink. 2023-02-09. Numerical RG-time integration of the effective potential: Analysis and Benchmark. https://doi.org/10.1103/physrevd.107.114009

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