O(N)-invariant Hierarchical Renormalization Group Fixed Points by Algebraic Numerical Computation and \epsilon-Expansion

TL;DR

This paper extends hierarchical renormalization group methods to compute O(N)-symmetric fixed points for various N and d, analyzing their spectra and critical exponents through algebraic numerical techniques and epsilon-expansion comparisons.

Contribution

It generalizes existing methods to N-component models and computes fixed points, spectra, and critical exponents for a range of N and d values.

Findings

Computed O(N)-symmetric fixed points for N=0 to 20 and d between 2 and 4.

Calculated spectra of linearized RG equations at fixed points.

Compared critical exponents with Borel-Pade-resummed epsilon-expansion results.

Abstract

Generalizing methods developed by Pinn, Pordt and Wieczerkowski for the hierarchical model with one component (N=1) and dimensions d between 2 and 4 we compute O(N)-symmetric fixed points of the hierarchical renormalization group equation for some N and d with 0 < d < 4 and -2 <= N <= 20. The spectra of the linearized RG equation at the fixed points are calculated and the critical exponents \nu are extracted from the spectrum and compared to Borel-Pade-resummed \epsilon-expansion.