Abstract
We apply pseudo-spectral methods to integrate functional flow equations with high accuracy, extending earlier work on functional fixed point equations \cite{Borchardt:2015rxa}. The advantages of our method are illustrated with the help of two classes of models: first, to make contact with literature, we investigate flows of the O$(N)$-model in 3 dimensions, for $N=1, 4$ and in the large $N$ limit. For the case of a fractal dimension, $d=2.4$, and $N=1$, we follow the flow along a separatrix from a multicritical fixed point to the Wilson-Fisher fixed point over almost 13 orders of magnitude. As a second example, we consider flows of bounded quantum-mechanical potentials, which can be considered as a toy model for Higgs inflation. Such flows pose substantial numerical difficulties, and represent a perfect test bed to exemplify the power of pseudo-spectral methods.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.