Pade-Borel approximation of the continuum limit of strong coupling lattice fields: Two dimensional non-linear O(N) sigma model at N>=3

TL;DR

This paper employs Pade-Borel approximants to analyze the continuum limit of the two-dimensional non-linear O(N) sigma model at N≥3, demonstrating consistency with continuum scaling and estimating the non-perturbative mass gap.

Contribution

It introduces a Pade-Borel approximation method to improve the strong coupling expansion analysis of the O(N) sigma model, aligning non-perturbative results with perturbative predictions.

Findings

Pade-Borel transformed coupling matches four-loop perturbation theory for N≥3.

Estimated mass gap agrees with known exact results.

Method improves understanding of continuum limit in lattice field theories.

Abstract

Based on the strong coupling expansion, we reinvestigate two dimensional O(N) sigma model by the use of Pade-Borel approximants. The conventional strong coupling expansion of the mass square M in momentum space in beta=1/g^2 is inverted to give beta expanded in 1/M. Borel transform of beta with respect to M is carried out and the result is improved as the rational function by Pade method. We find the behavior of Pade-Borel transformed bare coupling at 18th order is consistent for N>=3 with that of continuum scaling to the four-loop perturbation theory. We estimate non-perturbative mass gap at N>=3 and find the agreement with the exact result by Hasenfratz et.al.