New approach to Borel summation of divergent series and critical exponent estimates for an N-vector cubic model in three dimensions from five-loop \epsilon expansions

TL;DR

This paper introduces a novel Borel summation method using conformal mapping for divergent series, applied to estimate critical exponents in an N-vector cubic model from five-loop b b expansions, without requiring known asymptotic parameters.

Contribution

It presents a new Borel summation technique that does not depend on known asymptotic parameters, improving critical exponent estimates from high-order b expansions.

Findings

Effective summation of divergent series without asymptotic parameters

Accurate critical exponent estimates for N-vector cubic models

Method validated on functions with asymptotic power series

Abstract

A new approach to summation of divergent field-theoretical series is suggested. It is based on the Borel transformation combined with a conformal mapping and does not imply the exact asymptotic parameters to be known. The method is tested on functions expanded in their asymptotic power series. It is applied to estimating the critical exponent values for an N-vector field model, describing magnetic and structural phase transitions in cubic and tetragonal crystals, from five-loop \epsilon expansions.