Functional Renormalization Group meets Computational Fluid Dynamics: RG flows in a multi-dimensional field space
Abstract
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.
Cite
@article{arxiv.2412.16053,
title = {Functional Renormalization Group meets Computational Fluid Dynamics: RG flows in a multi-dimensional field space},
author = {Niklas Zorbach and Adrian Koenigstein and Jens Braun},
journal= {arXiv preprint arXiv:2412.16053},
year = {2024}
}