Functional Renormalization Group meets Computational Fluid Dynamics: RG flows in a multi-dimensional field space
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| Format: | Preprint |
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2024
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| _version_ | 1866909436447031296 |
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| author | Zorbach, Niklas Koenigstein, Adrian Braun, Jens |
| author_facet | Zorbach, Niklas Koenigstein, Adrian Braun, Jens |
| contents | Within the Functional Renormalisation Group (FRG) approach, we present a fluid-dynamical approach to solving flow equations for models living in a multi-dimensional field space. To this end, the underlying exact flow equation of the effective potential is reformulated as a set of nonlinear advection-diffusion-type equations which can be solved using the Kurganov-Tadmor central scheme, a modern finite-volume discretization from computational fluid dynamics (CFD). We demonstrate the effectiveness of our approach by performing explicit benchmark tests using zero-dimensional models with two discretized field space directions or two symmetry invariants. Our techniques can be directly applied to flow equations of effective potentials of general (fermion-)boson systems with multiple invariants or condensates, as we also demonstrate for two concrete examples in three spacetime dimensions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_16053 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Functional Renormalization Group meets Computational Fluid Dynamics: RG flows in a multi-dimensional field space Zorbach, Niklas Koenigstein, Adrian Braun, Jens Statistical Mechanics High Energy Physics - Phenomenology Within the Functional Renormalisation Group (FRG) approach, we present a fluid-dynamical approach to solving flow equations for models living in a multi-dimensional field space. To this end, the underlying exact flow equation of the effective potential is reformulated as a set of nonlinear advection-diffusion-type equations which can be solved using the Kurganov-Tadmor central scheme, a modern finite-volume discretization from computational fluid dynamics (CFD). We demonstrate the effectiveness of our approach by performing explicit benchmark tests using zero-dimensional models with two discretized field space directions or two symmetry invariants. Our techniques can be directly applied to flow equations of effective potentials of general (fermion-)boson systems with multiple invariants or condensates, as we also demonstrate for two concrete examples in three spacetime dimensions. |
| title | Functional Renormalization Group meets Computational Fluid Dynamics: RG flows in a multi-dimensional field space |
| topic | Statistical Mechanics High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2412.16053 |