Self-consistent renormalization group flow

TL;DR

This paper develops and compares a self-consistent renormalization group flow equation for scalar lambda phi^4 theory, analyzing critical exponents and optimizing convergence using the minimum sensitivity principle.

Contribution

It introduces a self-consistent RG flow equation, compares it with local potential approximation, and employs an optimization scheme for better convergence.

Findings

The flow equations coincide in the sharp cutoff limit.

Critical exponent nu depends on the smoothness parameter.

Optimization improves convergence of nu with polynomial truncation.

Abstract

A self-consistent renormalization group flow equation for the scalar lambda phi^4 theory is analyzed and compared with the local potential approximation. The two prescriptions coincide in the sharp cutoff limit but differ with a smooth cutoff. The dependence of the critical exponent nu on the smoothness parameter and the field of expansion is explored. An optimization scheme based on the minimum sensitivity principle is employed to ensure the most rapid convergence of nu with the level of polynomial truncation.