Numerical RG-time integration of the effective potential

• Verfasst von: Ihssen, Friederike [VerfasserIn]
• Verfasst von: Sattler, Franz R. [VerfasserIn]
• Verfasst von: Wink, Nicolas [VerfasserIn]
• Titel: Numerical RG-time integration of the effective potential
• Titelzusatz: analysis and benchmark
• Verf.angabe: Friederike Ihssen, Franz R. Sattler, and Nicolas Wink
• E-Jahr: 2023
• Jahr: 7 June 2023
• Umfang: 22 S.
• Fussnoten: Gesehen am 18.08.2023
• Titel Quelle: Enthalten in: Physical review
• Ort Quelle: Ridge, NY : American Physical Society, 2016
• Jahr Quelle: 2023
• Band/Heft Quelle: 107(2023), 11 vom: Juni, Artikel-ID 114009, Seite 1-22
• ISSN Quelle: 2470-0029
• DOI: doi:10.1103/PhysRevD.107.114009
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1856521354

Abstract

We investigate the renormalization group (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 automatic differentiation 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.