Numerical RG-time integration of the effective potential: analysis and benchmark
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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
7 June 2023
|
| In: |
Physical review
Year: 2023, Volume: 107, Issue: 11, Pages: 1-22 |
| ISSN: | 2470-0029 |
| DOI: | 10.1103/PhysRevD.107.114009 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1103/PhysRevD.107.114009 Verlag, lizenzpflichtig, Volltext: https://link.aps.org/doi/10.1103/PhysRevD.107.114009 
|
| Author Notes: | Friederike Ihssen, Franz R. Sattler, and Nicolas Wink |
| Summary: | 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. |
|---|---|
| Item Description: | Gesehen am 18.08.2023 |
| Physical Description: | Online Resource |
| ISSN: | 2470-0029 |
| DOI: | 10.1103/PhysRevD.107.114009 |