Estimate of the Critical Exponents from the Field-Theoretical Renormalization Group: Mathematical Sense of the "Standard Values"

TL;DR

This paper presents new estimates of critical exponents using a novel summation method for divergent series in the field-theoretical renormalization group, achieving results close to standard values but with reduced uncertainty.

Contribution

It introduces a new summation technique for divergent series in the renormalization group and discusses the implications of oscillating contributions on critical exponent estimates.

Findings

New estimates closely match standard values

Lower uncertainty in critical exponents

Oscillating contributions may affect accuracy

Abstract

New estimates of the critical exponents have been obtained from the field-theoretical renormalization group using a new method for summing divergent series. The results almost coincide with the central values obtained by Le Guillou and Zinn-Justin (the so-called "standard values"), but have lower uncertainty. It has been shown that usual field-theoretical estimates implicitly imply the smoothness of the coefficient functions. The last assumption is open for discussion in view of the existence of the oscillating contribution to the coefficient functions. The appropriate interpretation of the last contribution is necessary both for the estimation of the systematic errors in the "standard values" and for a further increase in accuracy.