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Functional Renormalization Group meets Computational Fluid Dynamics: RG flows in a multi-dimensional field space
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Functional Renormalization Group meets Computational Fluid Dynamics: RG flows in a multi-dimensional field space
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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.
Forward citations
Cited by 3 Pith papers
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Quantum critical fan and emergent relativistic symmetry of two-dimensional Dirac semimetals
A functional-RG calculation maps the chiral Ising Gross-Neveu-Yukawa phase diagram, confirming emergent relativistic symmetry at the quantum critical point and 2D Ising behavior at the finite-temperature transition.
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A neural network that learns fRG flows from the equation residual, with a large-N analytic baseline, matches finite-difference and discontinuous-Galerkin solvers for O(N) models.
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Operator PIRGs complete the prior PIRG method by enabling computation of all correlation functions, demonstrated analytically in zero-dimensional phi^4 theory via vertex expansion to ten-point functions.
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