Towards an accurate determination of the critical exponents with the Renormalization Group flow equations

TL;DR

This paper develops nonperturbative flow equations for scalar field theory to accurately compute critical exponents, demonstrating reduced scheme dependence and agreement with other methods.

Contribution

It introduces new flow equations at next-to-leading order using proper time regulators, improving the precision of critical exponent determination.

Findings

Critical exponents become insensitive to cut-off width with narrower cut-offs.

Computed exponents agree well with other approaches.

Reduced scheme dependence enhances reliability of the results.

Abstract

The determination of the critical exponents by means of the Exact Renormalizion Group approach is still a topic of debate. The general flow equation is by construction scheme independent, but the use of the truncated derivative expansion generates a model dependence in the determination of the universal quantities. We derive new nonperturbative flow equations for the one-component, $Z_2$ symmetric scalar field to the next-to-leading order of the derivative expansion by means of a class of proper time regulators. The critical exponents $\eta$, $\nu$ and $\omega$ for the Wilson-Fisher fixed point are computed by numerical integration of the flow equations, without resorting to polynomial truncations. We show that by reducing the width of the cut-off employed, the critical exponents become rapidly insensitive to the cut-off width and their values are in good agreement with the results of entirely different approaches.