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Global solutions of functional fixed point equations via pseudo-spectral methods

By Julia Borchardt and Benjamin Knorr

Abstract

We apply pseudo-spectral methods to construct global solutions of functional renormalisation group equations in field space to high accuracy. For this, we introduce a basis to resolve both finite as well as asymptotic regions of effective potentials. Our approach is benchmarked using the critical behaviour of the scalar $O(1)$ model, providing results for the global fixed point potential as well as leading critical exponents and their respective global eigenfunctions. We provide new results for (1) multi-critical $O(1)$ models in fractional dimensions, (2) the three-dimensional Gross-Neveu model at both small and large $N$, and (3) the scalar-tensor model, also in three dimensions.Comment: 14 pages, 9 figures. v2: typos correcte

Topics: High Energy Physics - Theory
Publisher: 'American Physical Society (APS)'
Year: 2015
DOI identifier: 10.1103/PhysRevD.91.105011
OAI identifier: oai:arXiv.org:1502.07511

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