Optimization of Renormalization Group Flow

TL;DR

This paper investigates how different smooth smearing functions affect the convergence of renormalization group flow equations for scalar phi^4 theory, improving critical exponent calculations in three dimensions.

Contribution

It introduces a method to optimize the convergence of RG flow equations by tuning the smoothness of smearing functions, enhancing critical exponent estimates.

Findings

Convergence of the critical exponent nu can be improved by fine-tuning smearing function smoothness.

Numerical results for nu in three dimensions are obtained using a truncated series expansion.

The choice of smearing functions significantly impacts the accuracy of RG flow calculations.

Abstract

Renormalization group flow equations for scalar lambda Phi^4 are generated using three classes of smooth smearing functions. Numerical results for the critical exponent nu in three dimensions are calculated by means of a truncated series expansion of the blocked potential. We demonstrate how the convergence of nu as a function of the order of truncation can be improved through a fine tuning of the smoothness of the smearing functions.