Global solutions of functional fixed point equations via pseudospectral methods

Abstract

We apply pseudospectral methods to construct global solutions of functional renormalization 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 behavior 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) multicritical $O(1)$ 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.